Eric Perlmutter
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View article: An $L$-function Approach to Two-Dimensional Conformal Field Theory
An $L$-function Approach to Two-Dimensional Conformal Field Theory Open
We introduce a framework for two-dimensional conformal field theory (CFT) in the language of analytic number theory. Attached to the torus partition function of every two-dimensional CFT is a self-dual, degree-4 $L$-function of root number…
View article: Modular-Invariant Random Matrix Theory and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> Wormholes
Modular-Invariant Random Matrix Theory and Wormholes Open
We develop a nonperturbative definition of RMT2: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its n-point spectral correlations…
View article: Modular-invariant random matrix theory and AdS${}_3$ wormholes
Modular-invariant random matrix theory and AdS${}_3$ wormholes Open
We develop a non-perturbative definition of RMT${}_2$: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its $n$-point spectral corr…
View article: $\\mathrm{A}$ $\\mathrm{CFT}$ distance conjecture
$\\mathrm{A}$ $\\mathrm{CFT}$ distance conjecture Open
We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinit…
View article: Rigorous Holographic Bound on AdS Scale Separation
Rigorous Holographic Bound on AdS Scale Separation Open
We give an elementary proof of the following property of unitary, interacting four-dimensional N=2 superconformal field theories: At large central charge c, there exist at least c single-trace, scalar superconformal primary operators with …
View article: AdS3/RMT2 duality
AdS3/RMT2 duality Open
A bstract We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS 3 quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for chaotic quantum systems, which origi…
View article: Exact large charge in $$ \mathcal{N} $$ = 4 SYM and semiclassical string theory
Exact large charge in $$ \mathcal{N} $$ = 4 SYM and semiclassical string theory Open
A bstract In four-dimensional $$ \mathcal{N} $$ = 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 arbit…
View article: AdS$_3$ Pure Gravity and Stringy Unitarity
AdS$_3$ Pure Gravity and Stringy Unitarity Open
We construct a unitary, modular-invariant torus partition function of a\ntwo-dimensional conformal field theory with a Virasoro primary spectral gap of\n$\\Delta_* = \\frac{c-1}{12}$ above the vacuum. The twist gap is identical, apart\nfro…
View article: AdS$_3$ Pure Gravity and Stringy Unitarity
AdS$_3$ Pure Gravity and Stringy Unitarity Open
We construct a unitary, modular-invariant torus partition function of a two-dimensional conformal field theory with a Virasoro primary spectral gap of $Δ_* = \frac{c-1}{12}$ above the vacuum. The twist gap is identical, apart from two stat…
View article: AdS$_3$/RMT$_2$ Duality
AdS$_3$/RMT$_2$ Duality Open
We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS$_3$ quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for chaotic quantum systems, which originates fr…
View article: Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs
Model-dependence of minimal-twist OPEs in d > 2 holographic CFTs Open
Following recent work on heavy-light correlators in higher-dimensional conformal field theories (CFTs) with a large central charge CT, we clarify the properties of stress tensor composite primary operators of minimal twist, [Tm], using arg…
View article: Discreteness and integrality in Conformal Field Theory
Discreteness and integrality in Conformal Field Theory Open
Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for th…
View article: Unitarity methods in AdS/CFT
Unitarity methods in AdS/CFT Open
We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on …
View article: Beyond a = c : gravitational couplings to matter and the stress tensor OPE
Beyond a = c : gravitational couplings to matter and the stress tensor OPE Open
We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large N CFTs with a large gap to single-trace higher spin operators, the s…
View article: Double-trace flows and the swampland
Double-trace flows and the swampland Open
We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconf…
View article: Constraints on higher spin CFT<sub>2</sub>
Constraints on higher spin CFT<sub>2</sub> Open
We derive constraints on two-dimensional conformal field theories with higher spin symmetry due to unitarity, modular invariance, and causality. We focus on CFTs with WN symmetry in the “irrational” regime, where c > N – 1 and the theories…
View article: Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory
Exact Large Charge in $\mathcal{N}=4$ SYM and Semiclassical String Theory Open
In four-dimensional $\mathcal{N}=4$ 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. The…
View article: Integrated correlators in $$ \mathcal{N} $$ = 4 SYM via SL(2, ℤ) spectral theory
Integrated correlators in $$ \mathcal{N} $$ = 4 SYM via SL(2, ℤ) spectral theory Open
A bstract We perform a systematic study of integrated four-point functions of half-BPS operators in four-dimensional $$ \mathcal{N} $$ = 4 super Yang-Mills theory with gauge group SU( N ). These observables, defined by a certain spacetim…
View article: Integrated Correlators in $\\mathcal{N}=4$ SYM via $SL(2,\\mathbb{Z})$\n Spectral Theory
Integrated Correlators in $\\mathcal{N}=4$ SYM via $SL(2,\\mathbb{Z})$\n Spectral Theory Open
We perform a systematic study of integrated four-point functions of half-BPS\noperators in four-dimensional $\\mathcal{N}=4$ super Yang-Mills theory with\ngauge group $SU(N)$. These observables, defined by a certain spacetime integral\nof …
View article: Virasoro conformal blocks in closed form
Virasoro conformal blocks in closed form Open
Virasoro conformal blocks are fixed in principle by symmetry, but a closed-form expression is unknown in the general case. In this work, we provide three closed-form expansions for the four-point Virasoro blocks on the sphere, for arbitrar…
View article: Growing extra dimensions in AdS/CFT
Growing extra dimensions in AdS/CFT Open
What is the dimension of spacetime? We address this question in the context of the AdS/CFT Correspondence. We give a prescription for computing the number of large bulk dimensions, D, from strongly-coupled CFTd data, where “large” means pa…
View article: The conformal bootstrap at finite temperature
The conformal bootstrap at finite temperature Open
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local o…
View article: Witten diagrams revisited: the AdS geometry of conformal blocks
Witten diagrams revisited: the AdS geometry of conformal blocks Open
Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the questio…
View article: Small black holes and near-extremal CFTs
Small black holes and near-extremal CFTs Open
Pure theories of AdS3 quantum gravity are conjectured to be dual to CFTs with sparse spectra of light primary operators. The sparsest possible spectrum consistent with modular invariance includes only black hole states above the vacuum. Wi…
View article: Loops in AdS from conformal field theory
Loops in AdS from conformal field theory Open
We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely une…
View article: Snowmass White Paper: Bootstrapping String Theory
Snowmass White Paper: Bootstrapping String Theory Open
We discuss progress and prospects in the application of bootstrap methods to string theory.
View article: Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings Open
We develop a new approach to extracting the physical consequences of S-duality of four-dimensional $\mathcal{N}=4$ super Yang-Mills (SYM) and its string theory dual, based on $SL(2,\mathbb{Z})$ spectral theory. We observe that CFT observab…