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Search: authors:"Shu-Heng Shao"

10 papers found.
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Surface defect indices and 2d-4d BPS states

We conjecture a formula for the Schur index of four-dimensional \( \mathcal{N}=2 \) theories coupled to (2, 2) surface defects in terms of the 2d-4d BPS spectrum in the Coulomb phase of the theory. The key ingredient in our conjecture is a refined 2d-4d wall-crossing invariant, which we also formulate. Our result intertwines recent conjectures expressing the four-dimensional...

Surface defects and chiral algebras

We investigate superconformal surface defects in four-dimensional \( \mathcal{N}=2 \) superconformal theories. Each such defect gives rise to a module of the associated chiral algebra and the surface defect Schur index is the character of this module. Various natural chiral algebra operations such as Drinfeld-Sokolov reduction and spectral flow can be interpreted as constructions...

(2, 2) superconformal bootstrap in two dimensions

We find a simple relation between two-dimensional BPS \( \mathcal{N}=2 \) superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2, 2) superconformal theories numerically with semidefinite programming. We constrain gaps in the non-BPS spectrum through the operator product expansion of...

Infrared computations of defect Schur indices

We conjecture a formula for the Schur index of four-dimensional \( \mathcal{N}=2 \) theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free...

\( \mathcal{N} \) = 4 superconformal bootstrap of the K3 CFT

We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS \( \mathcal{N} \) = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the...

Schur indices, BPS particles, and Argyres-Douglas theories

We conjecture a precise relationship between the Schur limit of the superconformal index of four-dimensional \( \mathcal{N}=2 \) field theories, which counts local operators, and the spectrum of BPS particles on the Coulomb branch. We verify this conjecture for the special case of free field theories, \( \mathcal{N}=2 \) QED, and SU(2) gauge theory coupled to fundamental matter...

Interpolating the Coulomb phase of little string theory

We study up to 8-derivative terms in the Coulomb branch effective action of (1, 1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST...

Supersymmetry Constraints and String Theory on K3

We study supervertices in six dimensional (2, 0) supergravity theories, and derive supersymmetry non-renormalization conditions on the 4- and 6-derivative four-point couplings of tensor multiplets. As an application, we obtain exact non-perturbative results of such effective couplings in type IIB string theory compactified on K3 surface, extending previous work on type II...

A low temperature expansion for matrix quantum mechanics

We analyze solutions to loop-truncated Schwinger-Dyson equations in massless \( \mathcal{N}=2 \) and \( \mathcal{N}=4 \) Wess-Zumino matrix quantum mechanics at finite temperature, where conventional perturbation theory breaks down due to IR divergences. We find a rather intricate low temperature expansion that involves fractional power scaling in the temperature, based on a...

Little string amplitudes (and the unreasonable effectiveness of 6D SYM)

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in \( \mathcal{N} \) = 2 minimal models. The results are expressed in terms of integrals of...