Giant Vortices and the Regge Limit

Cuomo, Gabriel; Komargodski, Zohar

doi:10.1007/jhep01(2023)006

“…Particularly related to our study, the large-charge limit has been studied in the context of extremal correlators in N = 2 supersymmetric theories, which can also be computed using supersymmetric localisation, see e.g. [30][31][32][33][34][35][36][37][38]. We find that, for the integrated correlators in N = 4 SYM that are considered in this paper, the large-p expansion takes a universal form, summarised in (4.32), and contains three parts.…”

Section: Jhep07(2023)129mentioning

confidence: 76%

Generating functions and large-charge expansion of integrated correlators in 𝒩 = 4 supersymmetric Yang-Mills theory

Brown

¹

,

Wen

²

,

Xie

³

2023

J. High Energ. Phys.

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We recently proved that, when integrating out the spacetime dependence with a certain integration measure, four-point correlators $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p^{(i)}{\mathcal{O}}_p^{(i)}\right\rangle $$ O 2 O 2 O p i O p i in 𝒩 = 4 supersymmetric Yang-Mills theory with SU(N) gauge group are governed by a universal Laplace-difference equation. Here $$ {\mathcal{O}}_p^{(i)} $$ O p i is a superconformal primary with charge p and degeneracy i. These physical observables, called integrated correlators, are modular-invariant functions of Yang-Mills coupling τ. The Laplace-difference equation is a recursion relation that relates integrated correlators of operators with different charges. In this paper, we introduce the generating functions for these integrated correlators that sum over the charge. By utilising the Laplace-difference equation, we determine the generating functions for all the integrated correlators, in terms of the initial data of the recursion relation. We show that the transseries of the integrated correlators in the large-p (i.e. large-charge) expansion for a fixed N consists of three parts: 1) is independent of τ, which behaves as a power series in 1/p, plus an additional log(p) term when i = j; 2) is a power series in 1/p, with coefficients given by a sum of the non-holomorphic Eisenstein series; 3) is a sum of exponentially decayed modular functions in the large-p limit, which can be viewed as a generalisation of the non-holomorphic Eisenstein series. When i = j, there is an additional modular function of τ that is independent of p and is fully determined in terms of the integrated correlator with p = 2. The Laplace-difference equation was obtained with a reorganisation of the operators that means the large-charge limit is taken in a particular way here. From these SL(2, ℤ)-invariant results, we also determine the generalised ’t Hooft genus expansion and the associated large-p non-perturbative corrections of the integrated correlators by introducing λ = p$$ {g}_{YM}^2 $$ g YM 2 . The generating functions have subtle differences between even and odd N, which have important consequences in the large-charge expansion and resurgence analysis. We also consider the generating functions of the integrated correlators for some fixed p by summing over N, and we study their large-N behaviour, as well as comment on the similarities and differences between the large-p expansion and the large-N expansion.

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“…In fact, we find not only convexity, but a certain lower bound on the amount of convexity (2.16) 16. There are also some exceptional cases, such as the theory of free fermions, where there is no symmetry breaking and no Goldstone boson at all.…”

mentioning

confidence: 69%

“…However, it is natural to expect, and this is true in all the examples we know, that such a regime should appear already at Q ≫ 1, rather than being controlled by some other parameters. 16 The second reason is that it is not necessarily the case that the lowest dimension operators within a charge range share the same Goldstone boson realisation. So, the dual states to the operators would break the symmetry differently: they would have different combinations of fields obtaining expectation values.…”

Section: Discussionmentioning

confidence: 99%

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Goldstone Bosons and Convexity

Orlando¹,

Palti²

2023

Preprint

1

0

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We study the spectrum of scalar charged operators in Conformal Field Theories (cfts) with a U (1) global symmetry. The charged operators are dual, by the stateoperator correspondence, to homogenous charged states on the sphere. Such states can break the U (1) symmetry, and we define what we call the large f regime in the cft as one where the symmetry breaking scale is much higher than the scale of the cft sphere. In such a regime, there is (an approximate) Goldstone boson associated to the breaking. We show that consistency of the Goldstone boson physics implies that the spectrum of states, and therefore of operators, must be convex in charge.More precisely, we show that any family of operators of different charges, which are lowest dimension of their charge, and which additionally share the same realisation of the Goldstone boson in terms of the degrees of freedom of the cft, must be convex.

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“…While the regime of p ∼ N 2 is perhaps the most novel and physically interesting from the AdS/CFT perspective, the large charge (more generally, large quantum number) expansion of quantum and conformal field theories is a fascinating subject in and of itself; see e.g. [2][3][4][5][6][7][8][9][10][11][12] for a selection of work and [13] for a recent review. We thoroughly situate our results in this context.…”

Section: Introductionmentioning

confidence: 99%

Exact large charge in $$ \mathcal{N} $$ = 4 SYM and semiclassical string theory

Paul,

Perlmutter,

Raj

2023

J. High Energ. Phys.

18

0

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In four-dimensional $$ \mathcal{N} $$ 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 ~ N2 ≫ 1, holographically dual to a large charge regime of semiclassical type IIB string theory in AdS5 × S5. 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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Giant Vortices and the Regge Limit

Cited by 18 publications

References 77 publications

Generating functions and large-charge expansion of integrated correlators in 𝒩 = 4 supersymmetric Yang-Mills theory

Generating functions and large-charge expansion of integrated correlators in 𝒩 = 4 supersymmetric Yang-Mills theory

Goldstone Bosons and Convexity

Exact large charge in $$ \mathcal{N} $$ = 4 SYM and semiclassical string theory

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