U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space

TL;DR

This paper constructs exact solutions for instantons in N=1/2 super Yang-Mills theory on non(anti)commutative superspace, revealing deformations in moduli space geometry and symmetry properties with implications for string theory and gauge-gravity duality.

Contribution

It provides the first exact instanton solutions in N=1/2 superspace, analyzing their geometry and symmetry deformations due to non(anti)commutativity.

Findings

U(2) instanton solution has SO(4) symmetry with nonzero U(1) field strength.

U(N) solutions are deformed and polarized, losing full rotational symmetry.

Moduli space geometry is deformed from hyperbolic space, but volume measure remains unchanged.

Abstract

We construct the exact solution of one (anti)instanton in N=1/2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1/2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), SU(2) part of the solution is given by the standard (anti)instanton, but U(1) field strength also turns out nonzero. The solution is SO(4) rotationally symmetric. For gauge group U(N), in contrast to the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti)commutativity and fermion zero-modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti)commutativity. We compute the `information metric' of one (anti) instanton. We find that moduli space geometry is deformed from hyperbolic space (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti)commutativity. Implications to D-branes in Ramond- Ramond flux background and Maldacena's gauge-gravity correspondence are discussed.