Non-perturbative Dynamics in Gauge and String



Scientific activities of the various Research Units

The activities of the GAST project are focused on four main interconnected themes:
1.     Gauge/gravity dualities, strongly coupled systems and applied holography
2.      Non-pertubative methods for gauge theories in diverse dimensions:
a.     Supersymmetric and non-supersymmetric dualities 
b.     Integrability, Localization and Bootstrap 
c.     Solitons and Instantons 
3.     Quantum Gravity, Quantum information and Black-Holes
4.     Field theoretical methods for gravity
1.    Florence and Pisa units  
The Witten-Sakai-Sugimoto (WSS) model is, at the moment, the top-down holographic theory closest to planar QCD in the infrared, where one can address some open strong-coupling problems by using analytic techniques. In particular, it is interesting to discuss some features pertinent to the realm of nuclear physics and which have not been fully considered in this context yet.  In this set-up, one is guided by the well-known relation between the WSS model and the Skyrme model. This relation allows us to borrow many tools developed in the context of Skyrmions and solitons in general and directly apply the holographic approach. Just like baryons in the large-N limit emerge as solitons of the chiral Lagrangian, in the WSS model, they are identified with instantons of the holographic Lagrangian describing the mesonic sector. Recently the two groups have shown how classical nuclei with multiple baryons can be described in this limit. They have also explored the theta dependence of different observables in the holographic context, and in particular, they were able to estimate the electric dipole moment of nucleons and deuterons. They plan to continue expanding all possible links between the holographic QCD and Skyrme model. Lately, the Florence group has also aimed to extend the phenomenological applications of the WWS model in different directions. Their research turned towards building the first top-down holographic model of the QCD axion, achieving already exciting results. In the future, they also plan to explore the properties of axion models in promising bottom-up scenarios. Suitably tuning its parameters, the WSS model can be used as a proxy for strongly coupled hidden (dark) sectors. Like in most BSM set-ups, the model experiences various first-order phase transitions at finite temperature triggering the production of gravitational waves, which, hopefully, can be detected in future experiments. A bonus of this analysis is that with a known top-down holographic description, the WSS model allows us to perform reliable calculations with control over the related approximations.
2.  Bologna, Firenze, Parma, Pisa and Trieste units
a.     Supersymmetric and non-supersymmetric dualities (Trieste and Pisa).
One of the primary themes of the recent research has been the infrared behavior of gauge theories in 2+1 and 3+1 dimensions with and without supersymmetry. Many new and exciting results have already been achieved.  The Trieste unit's goal is to find non-supersymmetric analogs (or deformations) of the exact results known for supersymmetric theories in 2+1 and 3+1 dimensions. These results should give new insights into the infrared dynamics of 2+1 dimensional theories and the boundary conditions/domain walls possible in 3+1 dimensional theories. Hopefully, it will be possible to obtain new exact results for 3+1dimensional gauge theories, such as finding new infrared dualities or determining the size of the conformal window in QCD.
The above dualities exchanging local operators with extended objects have naturally suggested the existence of generalized symmetries that act on extended objects rather than local fields.  Pisa unit tries to exploit them to investigate chiral gauge theories. Specifically, they shall take a few, simple chiral gauge theories as exercise grounds, and ask whether they can usefully apply these new theoretical tools to them. Mixed 't Hooft anomalies between 1-form symmetries and some 0-form (standard), in some cases, might give a decisive indication to select only a few possibilities for the infrared phase of the theory. Success in this direction represents a first hint that this approach can yield many significant results in a larger class of chiral gauge theories.
b.     Integrability, Localization and boostrap (Bologna, Firenze, Parma and Trieste).
Localization offers the unique opportunity to study the full non-perturbative answer for a restricted class of observables, such as partition functions on compact manifolds and line-operators in the case of supersymmetric field theories. The first topic we shall address is the long-standing problem of localizing N=2 supersymmetric gauge theories on compact toric manifolds.  Trieste unit made promising advances, and it plans to further investigate this problem for U(N) gauge theories in the presence of matter. Supersymmetric localization is particularly efficient also for studying two-dimensional non-supersymmetric theories. The prototypical example is pure Yang-Mills theory on compact Riemann surfaces. Parma and Florence unit aim to recover classical Witten's exact results in the framework of supersymmetric localization for the partition functions and the Wilson loops. The same type of investigations can then be extended to more sophisticated theories as CPN models. Bologna, Parma and Firenze are investigating the possibility of obtaining exact results by applying localization techniques to line defects in three dimensions. In particular, we would like to derive a previously conjectured matrix-model, describing "latitude" Wilson loops in ABJM theory. More generally, they plan to study the dualities properties of Wilson and vortex loops, and their bound states, in N=4 theories in three dimensions. Using supersymmetric localization, an effective description through topological quantum mechanics should be obtained. The same groups is considering N=4 SYM in the presence of codimension-one defects, preserving part of the superconformal symmetry. An interesting model is dual to the D3-D5 brane system with k units of flux, and its BPS sector can be studied through localization techniques. We aim to derive exact expressions for BPS Wilson loops and bulk to boundary correlation functions, confronting them with previous results derived through perturbation theory and AdS/CFT correspondence.
Integrability is another non-perturbative paradigm that emerged as the underlying structure behind the solvability of N=4 SYM and its deep relation with strings in AdS5xS5. It also appeared useful in relating theories with lower supersymmetry to two-dimensional systems amenable to exact computations. In this context, Bologna and Trieste units aim to deepen its incarnation in N=2 supersymmetric gauge theories. They plan to investigate the exact spectrum of superconformal field theories in five dimensions and their relevant deformations in terms of BPS quivers. They also aim to formulate a quiver's discrete dynamics in terms of q-difference equations, whose solutions in the various phases and duality frames of the theory should encompass and unify several different approaches developed so far as Nekrasov partition functions, matrix models and quantum Seiberg-Witten geometries. Another investigation in this framework concerns the gauge Painlevé correspondence: the partition function of some N=2 SYM theories coincides with the tau function of Painlevé equation. In this connection also the role of the corresponding topological string theory on Calabi-Yau threefolds is currently under scrutiny.
Bootstrap methods have instead found a new avatar in modern QFT, taking advantage of some analytical and numerical tools. When applied to (supersymmetric) conformal field theories, these techniques seem effectively able to chart the space of possible dynamics based on self-consistent hypotheses. Parma and Florence units plan to apply bootstrap in supersymmetric gauge theories. In four-dimensional N=4 SYM a large class of relevant defects is represented by 1/2 BPS line operators, as Wilson lines and ‘t Hooft lines: the two groups intend to deepen our knowledge of the related dCFT's using superconformal bootstrap and Witten diagrams techniques beyond leading orders, and, in collaboration with Bologna unit, to uncover the relation with the integrability approach performed through the  Quantum Spectral Curve. Parma and Florence units also continue their investigations on the dCFT1constructed through 1/2 BPS lines in ABJM theory. They plan to fully understand its topological sectors and explore the possibility to compute correlators there through localization, reproducing previously obtained bootstrap results. They intend to perform explicit weak coupling computation for the four-point correlation functions of the displacement operators to check some general Ward identities in this regime. Another goal is to chart the possible RG flows, connecting different dCFT1's hosted by ABJM Wilson loops, using bootstrap analysis 
c.     Solitons and Instantons (Trieste and Pisa)
Pisa unit also explores the role of solitons in effective models for QCD dynamics. In solitonic nuclear models, such as the Skyrme model, reproducing the small nuclear binding energies (%1 of the total) has been a constant challenge.   A possible solution is to consider near-BPS solitonic models, which are small perturbation around BPS models, where the energy is proportional to the topological charge (the baryon number), and so there is no binding energy between the nuclei. This unit plans to investigate the different aspects of this type of mechanism in a toy model given by the so-called baby-Skyrme. Building on this experience, they are trying to extend the analysis to several near-BPS solitonic models to select the most suitable ones for phenomenological applications. It would be attractive to classify all different types of near-BPS behaviors.
"Trieste unitl keeps developing research on moduli spaces of instantons in supersymmetric theories: an approach to building monads for framed sheaves using exceptional collections in the derived category is under scrutiny. Applications to the construction of moduli spaces of framed sheaves (resolutions of moduli spaces of instantons) and the computation of gauge theory partition functions is also part of the project. They also investigate certain classes of enumerative problems in string theory and in supersymmetric gauge theories associated with the counting of  D-branes bound states, which are strictly connected to either a K-theoretic version of theoretic Donaldson-Thomas theory of Calabi-Yau quivers or the combinatorial problem of enumerating colored solid partitions. Solitons and instantons in non-commutative theories are under scrutiny as well.
3.     Bologna, Firenze, Parma and Perugia units
Entanglement is not enough to understand the rich geometric structures that exist behind the horizon and which are predicted by general relativity. Thus, Susskind has introduced a new actor into the game, the quantum circuit complexity. There are two main proposals for the gravitational observables, which would be dual in holography to the complexity of a boundary state, complexity=volume, and complexity=action.  Despite this, the research about this quantity is still in its infancy. An essential shortcoming is that we lack a proper understanding of the circuit complexity in QFTs. Hence, it is necessary to develop the concept of circuit complexity for QFT fully. Most of the efforts in this direction have focused on QFT Gaussian states, where the prospect of comparing with holographic findings is somewhat unsatisfactory. Less progress has so far been achieved in defining complexity directly in conformal field theory (CFT). One compelling question that all the four groups would like to attack is building on these early results and exploiting conformal symmetry to explore viable notions of complexity in CFT. Cross-referencing with a large number of holographic results is used to constrain these measures and to understand whether any of them could be compatible with one of the proposed holographic realization of complexities.
Over the past few years, the long-term study of holographic entanglement entropy has allowed making some progress towards the resolution of the black hole information paradox. Lately, the Page curve for the evaporation process has been reproduced for lower dimensional models of gravity, paving the way to a full understanding of the paradox and its implications.  It would be interesting to approach different physical realizations of such systems to gain further insight. Moreover, the Page curve is only one manifestation of the paradox. One major question that all the four groups are addressing, is whether and how these new results reconcile with other formulations of the paradox, such as the one in terms of the late time decay of holographic correlators.
Jackiw-Teitelboim gravity in two dimensions provides a fruitful toy-model where many of the above questions can be studied concretely. First, exploiting localization, Firenze and Parma units reproduced the known results about its partition function and its correlators on the disk starting from its BF-formulation based on the group SL(2,R). Next, they are extending the analysis to the trumpet geometry through the introduction of vortex defect operators.  Theyl also investigate the supposed relation between boundary correlators and anchored Wilson lines as a tool to approach bulk physics directly from boundary dynamics. In this set-up, they are also directly examining a variety of quantum gravity aspects related to black-hole physics, chaos, and information theory.  Some of these features are also explored in AdS3 gravity: in particular, the computation of Wilson lines and their correlators.
4.     Bologna and Perugia units
The detection of gravitational waves by Ligo and Virgo has opened a new era in the investigation of gravitational dynamics. One of our aims is to deepen the understanding of the two-body problem in General Relativity using modern field theoretical S-matrix techniques. Several issues that deserve a better understanding arise when comparing the post-Newtonian (small velocity) and post-Minkowskian (small Newton's constant) approach to this problem. In particular, we plan to find a prescription for the post-Minkowskian expansion that is directly suited to reproducing the correct post-Newtonian contributions in the large speed of light limit and applying it to the case of two black holes with a very large mass hierarchy, which is relevant for future measurements at LISA.
Gravity amplitudes can also be studied on their own by first quantized methods, exploring in this context their relation with gauge-theory ones. 
Another application, where field theoretical techniques could fruitfully contribute is the description of the so-called Blandford-Znajek process taking place near the event horizon of a Kerr black-hole. The current approach is perturbative and mostly numeric. However, as recently pointed out, this description seems to have some problematic features.  We plan to attack this question by investigating the role of light-like surfaces in the solution of the equations of the force-free electrodynamics (FFE) (governing the magnetosphere). Secondly, exploiting the conformal symmetry emerging in the near extremal limit, we are constructing exact solutions of the FFE and extend them to physically relevant solutions using perturbative techniques.

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April, 20-21 2022

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