BPS states in (2,0) theory on R x T5

TL;DR

This paper investigates BPS states in (2,0) theory on R x T^5, analyzing their spectrum, symmetries, and invariance under deformations, using supersymmetry and connections to maximally supersymmetric Yang-Mills theory.

Contribution

It provides a detailed study of BPS states in (2,0) theory on R x T^5, including their spectrum, symmetry properties, and invariance, especially for the A-series, via supersymmetry and Yang-Mills theory.

Findings

Spectrum of BPS states characterized by momentum, flux, and R-symmetry.

Momentum obeys a flux-dependent shifted quantization law.

R-symmetry properties determined through representation ring analysis.

Abstract

We consider $(2, 0)$ theory on a space-time of the form $R \times T^5$, where the first factor denotes time, and the second factor is a flat spatial five-torus. In addition to their energy, quantum states are characterized by their spatial momentum, 't Hooft flux, and $Sp (4)$ $R$-symmetry representation. The momentum obeys a shifted quantization law determined by the 't Hooft flux. By supersymmetry, the energy is bounded from below by the magnitude of the momentum. This bound is saturated by BPS states, that are annihilated by half of the supercharges. The spectrum of such states is invariant under smooth deformations of the theory, and can thus be studied by exploiting the interpretation of $(2, 0)$ theory as an ultra-violet completion of maximally supersymmetric Yang-Mills theory on $R \times T^4$. Our main example is the $A$-series of $(2,0)$ theories, where such methods allow us to study the spectrum of BPS states for many values of the momentum and the 't Hooft flux. In particular, we can describe the $R$-symmetry transformation properties of these states by determining the image of their $Sp (4)$ representation in a certain quotient of the $Sp (4)$ representation ring.