On Higher Derivative Couplings in Theories with Sixteen Supersymmetries

TL;DR

The paper develops a framework of brane–bulk on-shell superamplitudes for a D3-brane in type IIB and extends it to torus-compactified 6D $(0,2)$ theories to derive non-renormalization theorems for higher-derivative couplings. By classifying F-term and D-term brane–bulk vertices, analyzing factorization, and applying soft theorems, it fixes the tau-dependent coefficients of $F^4$, $RF^2$, and $R^2$ couplings (e.g., $f_F$ constant, $f_1= frac{1}{2}Z_1$, $f_R$ harmonic with modular completion) and shows certain 5-point vertices cannot be local. The torus compactification analysis uses harmonicity on the Coulomb branch and interpolation through little string theory to determine the exact $F^4$ coefficient as a lattice sum $H(oldsymbol{ ho})$ and identifies the corresponding higher-dimensional operators, clarifying how SUSY and duality constrain these theories. Overall, the work provides precise, non-perturbative constraints that tie amplitudes, modular forms, and geometric moduli to the structure of higher-derivative couplings in highly supersymmetric theories.

Abstract

We give simple arguments for new non-renormalization theorems on higher derivative couplings of gauge theories to supergravity, with sixteen supersymmetries, by considerations of brane-bulk superamplitudes. This leads to some exact results on the effective coupling of D3-branes in type IIB string theory. We also derive exact results on higher dimensional operators in the torus compactification of the six dimensional (0, 2) superconformal theory.

Figures (10)

• Figure 1: Elementary supervertices. The wiggly line represents a bulk 1-particle state while the straight line represents a brane 1-particle state. The red dot represents the bulk vertex, whereas the blue and green dots are brane vertices.
• Figure 2: Factorization of the $R^2$ amplitude through elementary vertices. The red dot represents the bulk supergravity vertex whereas the blue and green dots are brane vertices.
• Figure 3: A factorization for the $RF^3$ superamplitude for the case of an Abelian gauge multiplet coupled to supergravity.
• Figure 4: A factorization for the $RF^3$ superamplitude for the case of an non-Abelian gauge multiplet coupled to supergravity.
• Figure 5: Single soft limit of ${\cal B}_{1,2}$.