String theory provides an elegant framework in which gravity and the other fundamental interactions of Nature are unified in a consistent (and presumably finite) quantum theory. In this framework, not only the traditional description of gauge and gravitational interactions in terms of a quantum field theory is recovered in the low-energy limit, but also unexpected connections between gauge and gravitational theories are revealed. These relationships, called dualities since they link the strong and weak coupling regimes of seemingly unrelated theories, are an important tool for investigating non-perturbative aspects that are out of reach for the standard methods.

The prototype of these relations is the Anti-de Sitter/Conformal Field Theory (AdS/CFT) duality between N=4 super Yang Mills theory in 4 dimensions and type IIB string in the AdS_{5} x S^{5} background. However, more general holographic correspondences can be established allowing to study the strong coupling limit of gauge theories by means of classical supergravity theories or, more generally, of strings propagating in non-trivial backgrounds and vice versa.

In the AdS/CFT correspondence a key role is played by the so-called “D-branes”, which are solitonic supergravity configurations where open strings can terminate and whose low-energy dynamics is described by quantum gauge theories. D-branes therefore represent the natural tool for studying gauge theories within string theory and their dual role as supergravity solitons leads directly to a relationship between gauge and gravity theories. Branes wrapping compact cycles have provided insights into the thermodynamics of black holes and have also been extensively used in numerous models of string phenomenology and string cosmology.

The purpose of this project is to investigate these multiple connections between string theory, quantum field theory and gravity from different perspectives, exploiting the complementary expertise of the participating units. In particular, our research program will be mainly focused on the following themes:

A) Supersymmetric quantum field theories

The study of quantum field theories beyond perturbation theory is essential since many physical phenomena, like for instance confinement or dynamical symmetry breaking, are governed by non-perturbative mechanisms. Furthermore, non-perturbative dynamics often includes beautiful physics and hidden mathematical structures, hardly visible from a perturbative point of view, which are not only interesting in their own right, but are also a key to perform explicit computations. We will address this problem mainly in the case of supersymmetric field theories, which usually exhibit interesting non-perturbative phenomena but are simpler to analyze than the non-supersymmetric ones.

The main tool that will be used to go beyond perturbation theory is holography combined with supersymmetric localization, bootstrap and integrability techniques. Within this framework we plan in particular:

● To study superconformal theories in 4d with and without defects, using localization, matrix model and integrability techniques, and derive exact expressions valid at all values of the coupling constant for local observables (such as chiral correlators, OPE coefficients, integrated correlators, etc.), and compare these results with those given in the dual holographic description. We will further analyze the link between holography and conformal bootstrap with the purpose of developing new methods based on the AdS/CFT correspondence combined with integrability to calculate correlation functions.

● To consider the role of extended excitations in the non-perturbative regime of superconformal theories. The synergic application of different techniques, such as conformal bootstrap, localization and holography can lead to new results especially for conformal defects, and reveal unexpected connections with quantum gravity and quantum information.

● To investigate the dynamics of superconformal field theories in diverse dimensions in order to establish a classification based on the correspondence with singular geometries in M-Theory, to search for interacting non-supersymmetric fixed points in 5d, and to study N=2 deformations of ADE N=4 supersymmetric theories in 3d.

B) Holography and quantum gravity

The AdS/CFT duality allows not only to understand the strong coupling dynamics of gauge theories from a gravitational perspective, but it can also be instrumental to shed light on other problems, like the computation of the entanglement entropy or the mechanisms that can lead to supersymmetry breaking in string theory. Another possibility, which recent advances in the field have made possible, is to use the AdS/CFT correspondence to study the dynamics of gravitational theories in terms of a dual CFT. While great progress has been obtained in recent years, much remains to be done. In this project we plan in particular:

● To study the quantum physics of black holes in AdS space, exploiting a fully-consistent non-perturbative formulation of quantum gravity through the AdS/CFT correspondence. Thanks to the synergy between holography and localization techniques one can study various properties of black holes in AdS spaces, and compute the quantum corrections to their entropy. More generally, we plan to use string theory and supersymmetric field-theory methods to analyze configurations of black holes and fuzzballs, to study the scattering of both massive and light states off black holes and the corresponding gravitational wave emissions.

● To undertake a comparative study of holography in AdS, de Sitter (dS) and flat spaces, with the aim of extending the definition of the holographic principle to more phenomenologically relevant backgrounds and of generalizing the techniques available in AdS to the more complex cases of dS and flat space holography. One of our long-term goals is also to provide a formulation of a non-perturbative holographic bootstrap for theories in dS and flat spaces.

● To study field theory in curved spaces, in particular in AdS backgrounds, with the idea of using boundary conformal correlators to understand strong coupling phenomena, and to compute late-time conformal correlators in dS backgrounds that are of interest to cosmology.

A) String phenomenology and string cosmology

String theory is known to lead to a landscape of 4d vacua with different phenomenological and cosmological features. Both top-down and bottom-up approaches to the string landscape can be helpful to make contact with testable predictions. Top-down constraints arising from the demand of compatibility with quantum gravity have recently received a lot of attention in the context of “swampland conjectures”. On the other hand, bottom-up approaches to the string landscape can be particularly useful to determine which phenomenological features are ubiquitous and which are typically stringy. We intend to use a combination of both approaches and in particular we plan:

● To study the role of dS space in string theory, as a possible string theory vacuum, with the ultimate goal of understanding its dynamics in terms of fundamental strings and branes.

● To study perturbative and non-perturbative corrections to string effective actions, and investigate their relevance for the process of moduli stabilization and the construction of realistic string vacua.

● To continue the efforts towards building Standard Model-like D-brane models in globally consistent compactifications of string theory, investigating explicit Calabi-Yau orientifold constructions to address problems in inflation, axion physics, dark matter and dark energy. Furthermore, since the construction of D-brane models in type IIB string theory describing stable dynamical supersymmetry breaking vacua has been recently extended to the so-called “large-N models”, we plan to investigate the geometries of CY singularities admitting brane configurations of this kind in order to construct their holographic dual.

A) Formal development in string theory

The investigation of the more formal aspects of string theory is an essential part for any research program in this field, since only a better knowledge of its internal structure can lead to significant improvement of its predictivity. All research units of this project will devote part of their activities to address these aspects that include the mathematical aspects of string theory in a broad sense. In particular we plan:

● To study the role of the generalized, higher form and non-invertible symmetries that have been recently introduced in field theory and string theory. We plan to investigate this problem both in two-dimensional and in higher dimensional theories, analyzing also the constraints that they impose on phenomenological model building and trying to understand their possible holographic interpretation.

● To study the structure and the underlying geometry of a string formulation that is manifestly invariant under T-duality and its generalizations, looking for connections with “double field theory” and generalized geometry. The role of integrability in these models will be a further possible development in this context.

● To investigate the semi-classical quantization of superstrings in curved backgrounds in general terms, since such studies can have relevant applications in the holographic framework.

● To work on various aspects of string field theory in order to sharpen the understanding of open-closed dynamics with the aim of understanding how the gauge/gravity duality can be encoded in the string field theory framework.

Our proposal aims to make progress in a quite broad area of research, and will address topics, from the more abstract and formal to the more phenomenological. The combination in this project of several groups with different backgrounds in quantum field theory and string theory aims to achieve better cross-fertilization between various research topics and enhance the scientific productivity of each research unit.

Many collaborations between research units of this project are already active, such as those between Trieste and Bologna, between Roma Tor Vergata and Torino and Napoli, and between Torino and Napoli, but to strengthen and extended them, we plan to organize joint activities and periodic meetings, and promote the mobility of participants.

We also plan to continue the cooperation between the INFN “Iniziative Specifiche” in formal high energy physics by cooperating in the organization of triangular bi-annual conferences (such as https://agenda.infn.it/event/20096/ and the previous ones).

Scientific activities of the various Research Units

INFN division BOLOGNA

The research activity of the Bologna unit will be focused on the study of phenomenological implications for particle physics, astrophysics and cosmology of the effective field theory in 4d obtained as the low energy limit of string compactifications. Both formal and phenomenological aspects of string compactifications, related to points C) and D) of the program will be discussed.

C) We plan to continue the study of the geometrical and topological structures of Calabi-Yau compactifications, focusing on the most promising ones for phenomenological applications. We will analyze physical consistency conditions and swampland constraints on the effective field theories emerging from different compactifications. We will also study the form of perturbative corrections to the Kähler potential and non-perturbative contributions to the superpotential of effective action of string compactifications. As far as phenomenological issues are concerned, we will instead analyze the stabilization of open and closed string moduli, paying particular attention to the realization of dS solutions. We will then proceed to the computation of moduli and axion mass spectra and of their couplings to both visible and hidden sector particles.

As regards applications to particle physics, we will work on Standard Model-like D-brane model-building in globally consistent compactifications. Instead, cosmological applications will focus on single-field and multi-field inflation and quintessence string models, early dark energy models from string moduli, the role played in cosmology by ultralight axions which are typical features of string compactifications, reheating after the end of string inflation and non-standard dark matter scenarios in string cosmology.

D) We will study the implications of higher-form and higher-group symmetries on various string compactifications and the constraints they impose on the resulting supersymmetric gauge and gravitational theories. The specific objectives concern the identification of structures encoding higher-form symmetries in string compactifications and their geometric and topological constraints, the formulation of anomaly arguments to provide a string-independent origin of these constraints, the definition of generic geometric features on the moduli space of conformal field theories based on higher-spin symmetries and emergent strings in holographic dual descriptions.

INFN division NAPOLI

The research activity of the Napoli unit will concentrate on points A), B) and D) of the program.

A) We plan to study Wilson loops and their correlators in supersymmetric Yang-Mills theories using the complementary approaches of holography and localization. In the holographic framework, systems can be described in terms of configurations of strings and branes, which can be studied using semi-classical methods. On the other hand, applying localization the problem is mapped to a matrix model. Employing previously developed combinatorial techniques as well as explicit matrix-model results, we plan to compute the sub-leading terms in the 1/N expansion of the Wilson loop correlators.

B) We will study how to extend the holographic principles to phenomenologically relevant contexts and try to transfer the techniques available in AdS to the more complex, but also more interesting cases of dS and flat space holography. We also plan to explore the quantum nature of black holes through an effective approach based on introducing quantum corrections to classical black hole solutions and organizing them in inverse powers of a physical distance. This procedure can be applied to study quantum corrections to Schwarzschild geometry and could be extended to Kerr geometry and gravitational waves.

D) One of our goals is to understand the underlying geometry of a string formulation manifestly invariant under T-duality and its generalizations, looking for connections with "dual field theory" and "generalized geometry". Some examples of world-sheet theories of strings, such as WZW sigma models, have already been discussed, and we now intend to extend our analysis to world- sheet actions describing non-geometric string backgrounds, such as those based on Poisson and Jacobi sigma models. The study of the classical integrability of these models will constitute a further development.

Another line of research will be focused on the study of massive higher-spin particles and their interactions with gravitons and photons. We plan to compute amplitudes involving such massive states in superstring theories using the so-called DDF operators and study their interactions with photons and gravitons, with the aim of gaining insight from string theory into the field theory description of Kerr black holes, and the string corrections to their interactions.

INFN division PADOVA

The research activity of the Padova unit will address mainly points A), B) and D) of the program.

A) We will study non-linear extensions of classical electrodynamics, such as the recently proposed ModMax theory and its Born-Infeld generalization. The relationship between this theory and the deformations of quantum field theories will also be analyzed; a first result of this study was the proposal of “Root-TTbar” deformations of two-dimensional QFTs. This is a marginal family of deformations that has a universal form when expressed in terms of the energy-stress tensor of a theory (like the well-known “TTbar” deformation). The relationship between Root-TTbar, ModMax and symmetries, especially integrability, needs to be better understood, as well as explored within the broader framework of string theory and holography. Applications of ModMax and its Born-Infeld generalization to the gravity/CMT correspondence will also be considered.

B) We will study two dimensional integrable QFTs (IQFTs) as well as conformal field theories in the context of holography, with particular focus on the AdS_{3}/CFT_{2} correspondence. These theories emerge both as dual CFTs and as theories on the string world sheet (IQFTs or CFTs). Using integrability, we recently proposed the equations for the spectrum of AdS_{3}/CFT_{2} with Ramond-Ramond fluxes. These equations need to be studied and generalized to even more general AdS_{3} setups. The structure of the dual theory and the role of integrability in its dynamics must also be understood.

D) We will study generalized and non-invertible symmetries in QFTs. Once again, an important case will be that of two-dimensional theories, which are under better control than higher-dimensional ones and have important applications to string theory. We will extend our study of string-theory orbifolds in the language of generalized symmetries to the case of non-abelian orbifolds, including the case where stringy dualities are non-trivially intertwined with the orbifold structure. This will provide a way to understand the twisted sectors of such theories, which is both important mathematically and useful for the construction of specific string models.

INFN division ROMA TOR VERGATA

The research activity of the Roma Tor Vergata unit will touch all points of the program.

A) We will continue to study applications of the Seiberg-Witten theory combined with localization, recursion relations and the AGT correspondence, to shed light on non-perturbative phenomena in QFTs that do not admit a Lagrangian description. One of the main objectives is the computation of observables such as the OPE coefficients of chiral operators in the regime of large charges. We also intend to study gauge theories with minimal supersymmetry in the context of string theory and achieve a geometric understanding of conformal dualities. Furthermore, we will investigate D3-brane field theories probing singular geometries in F-theory that preserve minimal supersymmetry, including theories that are intrinsically strongly coupled, such as those arising from so-called S-fold backgrounds.

B) We will analyze black-hole and fuzzball perturbations with particular attention to their relationship with the quantum Seiberg-Witten curves. We will also study the scattering off black holes in the Kerr-Schild gauge and the chaotic behavior of string amplitudes with highly excited states, investigating the validity of the effective field theory near the event horizons. We also intend to develop an approach to describe holographically dual theories in order to provide evidence for the conjecture that higher-spin gravity in 4d is dual to a higher-spin conformal gravity in 3d, realizing a fully nonlinear completion of the latter. Finally, we plan to study the production of gravitational waves in axion models, unified models and Majoron models, both at the perturbative and non-perturbative level, using holography.

C) We intend to discuss different aspects of quantum gravity models in which a dynamical torsion is present and study their phenomenological applications (coupling to the Standard Model, related inflationary cosmology, metric-affine generalizations with fermions, string- and brane-inspired models). We will also study the role of dS space in string theory in the context of bubble nucleation, with the aim of understanding its dynamics in terms of fundamental objects such as strings and branes. We will also continue our analysis of the alpha' corrections in the string effective actions and their implications for the construction of realistic string vacua within the Large Volume paradigm.

D) We will begin to explore the realm of generalized symmetries in quantum field theory, with the aim of finding possible phenomenological applications of the so-called non-invertible symmetries.

INFN division TORINO

The research activity of the Torino research unit will address points A) and D) of the program.

A) We intend to investigate the strongly coupled regime of QFTs using localization techniques and matrix models, focusing on theories with extended supersymmetry and/or conformal symmetry. In the arena of N=2 SCFTs in 4 dimensions admitting a holographic dual, we will study the large coupling expansion of observables such as chiral correlators and extremal correlators also in the presence of conformal defects. We will investigate their sub-leading contributions in the 1/N expansion and compare with the results obtained using holographic methods. Since extended observables such as Wilson loops or surface operators are important probes to explore the non-perturbative regime of QFTs, we will study these defects also in non-conformal N=2 theories to understand to what extent they are captured by localization.

The application of techniques, such as conformal bootstrap, supersymmetric localization, and holography, unveiled unexpected relationships between conformal defects, quantum gravity and quantum information. We would like to explore in more detail these connections by analyzing several examples of defects, such as twist operators, whose expectation value computes Rényi entanglement entropy, as well as boundaries and impurities in statistical systems that are also relevant for the condensed matter community. We will apply bootstrap techniques to the study of scattering amplitudes, renormalization group fluxes and defects. Specifically, we intend to focus on the scattering of particles with spin in flat space, including photons and gravitons, on strongly coupled renormalization group fluxes in AdS and on boundaries of two-dimensional irrational CFTs.

D) We intend to improve our understanding of open-closed string dynamics as described by open-closed string field theory (SFT). We will focus on studying how D-branes back-react to a new closed string background in specific examples, with the aim of understanding how the gauge/gravity duality is encoded in the SFT framework. Other lines of exploration will include the role of the ghost-dilaton theorem in the construction of string theory observables and background independence and the computation of D-instanton contributions to closed string scattering using Witten open SFT with Ellwood invariants to minimize the number of Feynman diagrams and take advantage of the infrared divergence regularization that is built into SFT.

We also intend to study how string theory can be used to understand spatial singularities, such as the Big Bang or the Big Crunch, and investigate if highly excited massive string states can capture the physics of Kerr black holes and see if the collisions of two of these states produce gravitational waves that differ from those of two black holes derived from general relativity.

INFN division TRIESTE

The research activity of the TRIESTE unit will touch all points of the program.

A) We plan to investigate various aspects of supersymmetric QFTs in different dimensions. In 4 dimensions, we will apply localization techniques with a two-fold purpose: to study the exact dependence on the so-called Omega-background of the partition function of supersymmetric strongly coupled theories of the Argyres-Douglas type, and to exactly calculate observables of boundary supersymmetric conformal field theory. In 5 dimensions, we will apply a recently introduced gauge theoretic approach to classify super CFT corresponding to specific singular geometries in M-theory. Moreover, by using brane-web techniques, we will study 5-dimensional QFTs to search for interacting non-supersymmetric fixed points. Finally, in 3 dimensions we plan to study N=2 deformations of ADE N=4 supersymmetric theories, which realize mathematically interesting singular geometries as their moduli space.

B) We will study QFTs in a curved space-time, both of AdS type, where we can use boundary conformal correlators to understand strong coupling phenomena, and of dS type, where we want to understand the general structure of late-time conformal correlators that are of interest to cosmology. We will also investigate the quantum physics of black holes in AdS, exploiting the non-perturbative formulation of quantum gravity given by the AdS/CFT correspondence and exploiting localization techniques to perform exact path-integral computations.

C) Since the construction of D-brane models in type IIB string theory describing stable dynamical supersymmetry breaking vacua has been recently extended to large N models, we will investigate the geometries of CY singularities admitting brane configurations of this kind to construct their holographic dual. Type IIB string theory with branes and orientifolds is also a good framework to construct realistic string models of particle physics in combination with moduli stabilization; to better describe the resulting effective 4D action, we plan to study its quantum corrections at leading order in alpha' and string coupling, understanding their implications on moduli stabilization.

D) Following the recent intense activity on higher form, higher group, and non-invertible symmetries, we plan to extend our preliminary results to understand these symmetries using holography, and to refine them using D-brane models in string theory. One of the main goals of this line of research will be to extend to these structures the fundamental concepts of representations, anomalies, symmetry breaking, etc.