The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories

TL;DR

The paper proposes an exact formula for the Bremsstrahlung function $B$ in four-dimensional ${\cal N}=2$ SCFTs, linking it to the Wilson line data via $B=3h_W=\frac{1}{4\pi^2}\partial_b\ln\langle W_b\rangle|_{b=1}$. It shows consistency with known ${\cal N}=4$ results, derives perturbative checks up to $g^6$, and analyzes nonperturbative effects through instantons and the 1-loop determinant. The results imply positivity of $B$, constrain matter-content dependence up to certain orders, and yield implications for entanglement entropy and transcendentality structure. Overall, the work provides a nonperturbative framework to predict energy radiation by accelerating quarks in ${\cal N}=2$ SCFTs and connects it to exact localization data on the ellipsoid.

Abstract

We propose an exact formula for the energy radiated by an accelerating quark in N=2 superconformal theories in four dimensions. This formula reproduces the known Bremsstrahlung function for N=4 theories and provides a prediction for all the perturbative and instanton corrections in N=2 theories. We perform a perturbative check of our proposal up to three loops.

Figures (5)

• Figure 1: Diagrams that contribute to ${\left< {O_2(x)W} \right>}$ and include hypermultiplet fields. In this figure gauge fields are denoted with wiggly line, scalar fields from the vector multiplet are denoted with double line, and hypermultiplet fields are denoted by a plain line (with an arrow for fermions and without an arrow for scalars).
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