Harnessing S-Duality in $\mathcal{N}=4$ SYM &amp; Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings

Collier, Scott; Perlmutter, Eric

doi:10.48550/arxiv.2201.05093

Cited by 4 publications

(21 citation statements)

References 149 publications

(293 reference statements)

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“…For N = 2, 3, we explicitly compute exponentially small corrections in λ p 1. These are controlled by the non-perturbative scale e − √ 2λp , a result correctly predicted by the weak coupling radius of convergence as a non-trivial consequence of S-duality [25].…”

Section: ) Solve the Recursion In Closed Formsupporting

confidence: 55%

“…p (1) is satisfied [25] by this solution. The Eisenstein overlaps (2.6) and (2.7) furnish the full solution for the integrated correlators for any p and N .…”

Section: Exact Solutionmentioning

confidence: 88%

“…In [1], we exploited this connection together with the fact that G (N ) p (τ ) can be very efficiently expressed in the SL(2, Z) spectral decomposition [25]. This expands G (N ) p (τ ) in an S-dualityinvariant, complete eigenbasis of the scalar Laplacian on H + :…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory

Paul¹,

Perlmutter²,

Raj³

2023

Preprint

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In four-dimensional N = 4 super Yang-Mills theory with gauge group SU (N ), we present a closed-form solution for a family of integrated four-point functions involving stress tensor multiplet composites of arbitrary R-charge. These integrated correlators are shown to be equivalent to a one-dimensional semi-infinite lattice of harmonic oscillators with nearest-neighbor interactions, evolving over the fundamental domain of SL(2, Z). The solution, exceptionally simple in an SL(2, Z)-invariant eigenbasis, is exact in the R-charge p, rank N , and complexified gauge coupling τ . This permits a systematic and non-perturbative large charge expansion for any N and τ . Especially novel is a double-scaled "gravity regime" in which p ∼ N 2 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS 5 × S 5 . Our results in this limit provide a holographic computation of integrated semiclassical string amplitudes at arbitrary string coupling, including an emergent string scale with a large charge dressing factor. We compare to extremal correlators in superconformal QCD, for which we predict new genus expansions at large charge scaling with N .

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Section: ) Solve the Recursion In Closed Formsupporting

confidence: 55%

“…p (1) is satisfied [25] by this solution. The Eisenstein overlaps (2.6) and (2.7) furnish the full solution for the integrated correlators for any p and N .…”

Section: Exact Solutionmentioning

confidence: 88%

See 1 more Smart Citation

Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory

Paul¹,

Perlmutter²,

Raj³

2023

Preprint

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“…refs. [52,[123][124][125][126][127][128]). On the other hand, a host of uncomfortable consequences reverberate outward from it, starting with the idea that since this implies that gravity is an ensemble, its holographic dual (in any dimension) must not have a definite Hamiltonian.…”

Section: Discussionmentioning

confidence: 99%

The Microstate Physics of JT Gravity and Supergravity

Johnson¹

2022

Preprint

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It is proposed that a complete understanding of two-dimensional gravity and its emergence in random matrix models requires fully embracing both Wigner (statistics) and 't Hooft (geometry). Using non-perturbative definitions of random matrix models that yield various JT gravity and JT supergravity models on surfaces of arbitrary topology, Fredholm determinants are used to extract precise information about the spectra of discrete microstates that underlie the physics. Smooth spacetime geometry emerges only when the gaps between microstates are negligible, and there are two complementary mechanisms that achieve this in matrix models. A core idea suggested by the computations is that in each case, the matrix models point to a single distinguished discrete spectrum that characterizes the holographic dual of the (super) gravity theory, living on the disc. Only asymptotically does it reduce to the effectively continuous (super) Schwarzian result. Several physical consequences of this are elucidated, including a reassessment of the factorization puzzle. It is entirely resolved if matrix models are recognized not as models of a single JT gravity theory but as describing an ensemble of JT deformations, each of whose holographic dual is a matrix. This would immediately explain why there is also no failure of factorization for traditional higher dimensional holographic duals. Several lessons that may pertain to quantum gravity on non-trivial topology in higher dimensions are noted, and a thorough introduction to the non-perturbative matrix model techniques used is included.

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“…5 These string corrections have been addressed in [28,29,30,31,32]. 6 The existence of such contributions ultimately follows from S-duality of type IIB string theory, see references [33,34,35] for a study of modular invariance in this context and also the recent work [36] for a new approach to SL(2, Z) invariance in the context of N = 4 SYM.…”

Section: Setup: Thementioning

confidence: 99%

Two-loop supergravity on AdS$_5\times$S$^5$ from CFT

Drummond,

Paul

2022

Preprint

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We describe a construction of the two-loop amplitude of four graviton supermultiplets in AdS 5 ×S 5 . We start from an ansatz for a preamplitude from which we generate the full amplitude under the action of a specific Casimir operator. The ansatz captures a recent ansatz of Huang and Yuan and we confirm their result through similar constraints. We identify a class of four-dimensional 'zigzag' integrals which are perfectly adapted to describing the leading logarithmic discontinuity to all orders. We also observe that a bonus crossing symmetry of the preamplitude follows from the transformation properties of the Casimir operator. Combined with the zigzag integrals this allows us to construct a crossing symmetric function with the correct leading logarithmic discontinuities in all channels.From the two-loop result we extract an explicit expression for the two-loop correction to the anomalous dimensions of twist-four operators of generic spin which includes dependence on (alternating) nested harmonic sums up to weight three. We also revisit the prescription of the bulk-point limit of AdS amplitudes and show how it recovers the full flat-space amplitude, not just its discontinuity. With this extended notion of the bulk-point limit we reproduce the scale-dependent logarithmic threshold terms of type IIB string theory in flat-space.

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Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings

Cited by 4 publications

References 149 publications

Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory

Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory

The Microstate Physics of JT Gravity and Supergravity

Two-loop supergravity on AdS$_5\times$S$^5$ from CFT

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