Motivated by quantum gravity and the CFT Distance Conjecture, we study infinite-distance limits in four-dimensional 𝒩 = 2 superconformal field theories with higher-dimensional conformal manifolds and their AdS duals. We focus on partial decoupling limits where a gauge sector becomes weakly coupled while an interacting sector persists.

Germany

Fabio Mantegazza

Enrico Marchetto

Elli Pomoni

Torben Skrzypek

Timo Weigand

Multiplet recombination and the CFT Distance Conjecture

We compute thermal holographic correlators by combining their analytic structure with the Kubo-Martin-Schwinger (KMS) condition and multi-stress tensor OPE coefficients determined from the dual AdS description. We focus on two-point functions of identical scalar operators with integer conformal dimensions at zero spatial separation. In the black brane background, we show explicitly that holographic two-point functions split into three contributions: a principal one, computed exactly, plus regularized and arcs contributions, both approximated through the use of OPE coefficients asymptotics. For ∆ = 3, we show that the principal contribution agree with good approximation with the numerical solution of the bulk wave equation. Moreover, we demonstrate that the expansion in generalized free field correlators proposed in [1] admits a natural interpretation in terms of Witten diagrams. Finally, we initiate the study of thermal correlators in the spherically symmetric black hole background, computing their principal contributions.

Julien Barrat

Deniz Bozkurt

United States

Alessio Miscioscia

Analytic thermal bootstrap meets holography

We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation result obtained in the OPE regime. This construction satisfies all thermal bootstrap conditions, with the exception of clustering at infinite distance, which must be verified on a case-by-case basis. We test our results both in weakly and strongly-coupled theories. In particular, we show that the asymptotic behavior for the heavy sector proposed in [1] and its correction can be explicitly derived from the dispersion relation. We combine analytical and numerical results to compute the thermal two-point function of the energy operator in the 3d Ising model and find agreement with Monte Carlo simulations.

The analytic bootstrap at finite temperature

<p>We propose a numerical method to estimate one-point functions and the free-energy density of conformal field theories at finite temperature by solving the Kubo-Martin-Schwinger condition for the two-point functions of identical scalars. We apply the method for the critical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> model for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math>, 2, 3 in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>3</mn><mo>≤</mo><mi>d</mi><mo>≤</mo><mn>4</mn></math>. We find agreement with known results from Monte Carlo simulations and previous results for the 3D Ising model, and we provide new predictions for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math>, 3.</p>

United Kingdom

Thermal Bootstrap for the Critical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math> Model

We explore the connection between super $$ \mathcal{W} $$ -algebras ( $$ \mathcal{SW} $$ -algebras) and G-structures with torsion. The former are realised as symmetry algebras of strings with $$ \mathcal{N} $$ = (1, 0) supersymmetry on the worldsheet, while the latter are associated with generic string backgrounds with non-trivial Neveu-Schwarz flux $\textit{H}$. In particular, we focus on manifolds featuring Spin(7), G , SU(2), and SU(3)-structures. We compare the full quantum algebras with their classical limits, obtained by studying the commutators of superconformal and $$ \mathcal{W} $$ -symmetry transformations — which preserve the action of the (1, 0) non-linear $\textit{σ}$-model. We show that, at first order in the string length scale $\textit{ℓ}$ , the torsion deforms some of the OPE coefficients corresponding to special holonomy through a scalar torsion class.

Xenia Ossa

Mateo Galdeano

$$ \mathcal{SW} $$ -algebras and strings with torsion

We study CFTs at finite temperature and derive explicit sum rules for one-point functions of operators by imposing the KMS condition and we explicitly estimate one-point functions for light operators. Turning to heavy operators we employ Tauberian theorems and compute the asymptotic OPE density for heavy operators, from which we extract the leading terms of the OPE coefficients associated with heavy operators. Furthermore, we approximate and establish bounds for the two-point functions.

Sum rules &amp; Tauberian theorems at finite temperature

When a (super) conformal field theory is placed on a non-trivial manifold, the (super) conformal symmetry is broken. However, it is still possible to derive broken Ward identities for these broken symmetries, which provide additional constraints on the theory. We derive and apply the broken Ward identities associated with the (super) conformal group on the thermal manifold   <math> <msub> <mi>M</mi> <mi>β</mi> </msub> <mo>=</mo> <msubsup> <mi>S</mi> <mi>β</mi> <mn>1</mn> </msubsup> <mo>×</mo> <msup> <mi>ℝ</mi> <mrow> <mi>d</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </math>  $$ {\mathcal{M}}_{\beta }={S}_{\beta}^1\times {\mathbb{R}}^{d-1} $$  and   <math> <mi>M</mi> <mo>=</mo> <msup> <mi>T</mi> <mn>2</mn> </msup> <mo>×</mo> <msup> <mi>ℝ</mi> <mrow> <mi>d</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> </math>  $$ \mathcal{M}={T}^2\times {\mathbb{R}}^{d-2} $$ . The novel constraints not only systematically reproduce known results, including an implicit formulation of the generalized Cardy formula, but also elegantly relate the thermal energy spectrum with the conformal spectrum.

Broken (super) conformal Ward identities at finite temperature

We consider current-current deformations that generalize <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math> ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the deformation as a modification of the <math><mrow><mi>S</mi></mrow></math> matrix in the Bethe equations. Using results by Bargheer, Beisert and Loebbert we show that the deforming operator is composite and constructed out of two currents on the lattice; its expectation value factorizes like for <math><mi>T</mi><mover><mi>T</mi><mo>¯</mo></mover></math>. Such a deformation may be considered for any combination of charges that preserve the model’s integrable structure.