Correlators in N=1 SYM(2+1)

TL;DR

This paper calculates a specific correlator in 2+1 dimensional N=1 supersymmetric Yang-Mills theory using SDLCQ, revealing behavior at different scales and a critical coupling where the correlator vanishes.

Contribution

It applies supersymmetric discrete light-cone quantization to compute correlators in N=1 SYM(2+1), preserving supersymmetry and analyzing large and small distance behaviors.

Findings

Correlator behaves as 1/r^6 at small r.

At large r, the correlator is dominated by BPS states.

Identifies a critical coupling where the correlator approaches zero.

Abstract

We present a calculation of the correlator <0|T^{++}(r) T^{++}(0) |0> in N=1 SYM theory in 2+1 dimensions. In the calculation, we use supersymmetric discrete light-cone quantization (SDLCQ), which preserves the supersymmetry at every step of the calculation. For small and intermediate r the correlator converges rapidly for all couplings. At small r the correlator behaves like 1/r^6, as expected. At large r the correlator is dominated by the BPS states of the theory. We find a critical coupling where the large-r correlator goes to zero; it grows like the square root of the transverse cutoff.