Exact TTˉT\bar{T}-deformation of two-dimensional Yang-Mills theory on the sphere

We study the $T\bar{T}$ deformation of two-dimensional Yang-Mills theory at genus zero by carrying out the analysis at the level of its instanton representation. We first focus on the perturbative sector by considering its power expansion in the deformation parameter $\mu$. By studying the resulting asymptotic series through resurgence theory, we determine the nonperturbative contributions that enter the result for $\mu<0$. We then extend this analysis to any flux sector by solving the relevant flow equation. Specifically, we impose boundary conditions corresponding to two distinct regimes: the quantum undeformed theory and the semiclassical limit of the deformed theory. The full partition function is obtained as a sum over all magnetic fluxes. For any $\mu>0$, only a finite portion of the quantum spectrum survives and the partition function reduces to a sum over a finite set of representations. For $\mu<0$, nonperturbative contributions regularize the partition function through an intriguing mechanism that generates nontrivial subtractions.Comment: 36 pages, 4 figure

The resurgence of the plateau in supersymmetric N=1{\cal N}=1 Jackiw-Teitelboim gravity

Significant progresses have been made recently in understanding the spectral form factor of Jackiw-Teitelboim gravity, particularly at late times where non-perturbative effects are expected to play a dominant role. By focusing on a peculiar regime of large time and fixed temperature, called $\tau$-scaling limit, it was found that it is possible to analytically investigate the late-time plateau directly through the gravitational genus expansion. We extend this analysis to the supersymmetric $\mathcal{N}=1$ generalization of the bosonic theory, revealing an interesting structure. First, we notice that in the $\tau$-scaling limit the perturbative sum over genera truncates after a single term, which solely accounts for the ramp behaviour. Instead a non-perturbative completion, responsible for the plateau, is encoded into an exact formula coming from the properties of the chiral gaussian ensemble, governing the spectral properties of the supersymmetric theory. We are able to recover the non-perturbative contributions by slightly deforming the genus of the involved surfaces and using resurgence theory. We derive a closed-form analytical expression for the late-time plateau and a trans-series expansion that captures the ramp-plateau transition.Comment: 35 pages, 7 figure

Localization and resummation of unstable instantons in 2d Yang-Mills

We compute the exact all-orders perturbative expansion for the partition function of 2d $\mathrm{SU}(2)$ Yang-Mills theory on closed surfaces around higher critical points. We demonstrate that the expansion can be derived from the lattice partition function for all genera using a distributional generalization of the Poisson summation formula. We then recompute the expansion directly, using a stationary phase version of supersymmetric localization. The result of localization is a novel effective action which is itself a distribution rather than a function of the supersymmetric moduli. We comment on possible applications to A-twisted models and their analogs in higher dimensions.Comment: 35 page

Supersymmetric localization of (higher-spin) JT gravity: a bulk perspective

We study two-dimensional Jackiw-Teitelboim gravity on the disk topology by using a BF gauge theory in the presence of a boundary term. The system can be equivalently written in a supersymmetric way by introducing auxiliary gauginos and scalars with suitable boundary conditions on the hemisphere. We compute the exact partition function thanks to supersymmetric localization and we recover the result obtained from the Schwarzian theory by accurately identifying the physical scales. The calculation is then easily extended to the higher-spin generalization of Jackiw-Teitelboim gravity, finding perfect agreement with previous results. We argue that our procedure can also be applied to boundary-anchored Wilson line correlators.Comment: 29 page

The phase diagram of T(T)over-bar-deformed Yang-Mills theory on the sphere

We study the large-N dynamics of T (T) over bar -deformed two-dimensional Yang-Mills theory at genus zero. The 1/N-expansion of the free energy is obtained by exploiting the associated flow equation and the complete phase diagram of the theory is derived for both signs of the rescaled deformation parameter tau. We observe a third-order phase transition driven by instanton condensation, which is the deformed version of the familiar DouglasKazakov transition separating the weakly-coupled from the strongly-coupled phase. By studying these phases, we compute the deformation of both the perturbative sector and the Gross-Taylor string expansion. Nonperturbative corrections in tau drive the system into an unexplored disordered phase separated by a novel critical line meeting tangentially the Douglas-Kazakov one at a tricritical point. The associated phase transition is induced by the collision of large- N saddle points, determining its second-order character

Exact T¯T Deformation of Two-Dimensional Maxwell Theory

We study the partition function of T¯T-deformed two-dimensional Maxwell theory by solving the relevant flow equation at the level of individual flux sectors. Summing exactly the “instanton” series, we obtain a well-defined expression for the partition function at arbitrary μ. For μ&gt;0, the spectrum of the theory experiences a truncation and the theory undergoes infinite-order quantum phase transitions associated with the vanishing of Polyakov-loop correlators. For μ&lt;0, the appearance of nonperturbative contributions in μ drastically modifies the structure of the partition function.Title in Web of Science: Exact T(T)over-bar Deformation of Two-Dimensional Maxwell Theory</p

Nonperturbative effects and resurgence in Jackiw-Teitelboim gravity at finite cutoff

We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a T (T) over bar -deformed Schwarzian quantum mechanics. Our starting point is a careful computation of the disk partition function to all orders in the perturbative expansion in the cutoff parameter. We show that the perturbative series is asymptotic and that it admits a precise completion exploiting the analytical properties of its Borel transform, as prescribed by resurgence theory. The final result is then naturally interpreted in terms of the nonperturbative branch of the T (T) over bar -deformed spectrum. The finite-cutoff trumpet partition function is computed by applying the same strategy. In the second part of the paper, we propose an extension of this formalism to arbitrary topologies, using the basic gluing rules of the undeformed case. The Weil-Petersson integrations can be safely performed due to the nonperturbative corrections and give results that are compatible with the flow equation associated with the T (T) over bar deformation. We derive exact expressions for general topologies and show that these are captured by a suitable deformation of the Eynard-Orantin topological recursion. Finally, we study the "slope" and "ramp" regimes of the spectral form factor as functions of the cutoff parameter

Localization and resummationof unstable instantons in 2d Yang-Mills

We compute the exact all-orders perturbative expansion for the partition function of 2d SU(2) Yang-Mills theory on closed surfaces around higher critical points of the classical action. We demonstrate that the expansion can be derived from the lattice partition function for all genera using a distributional generalization of the Poisson summation formula. We then recompute the expansion directly, using a stationary phase version of supersymmetric localization. The result of localization is a novel effective action which is itself a distribution rather than a function of the supersymmetric moduli. We comment on possible applications to A-twisted models and their analogs in higher dimensions.</p