Two-Point Stress-Tensor Correlator in N=1 SYM(2+1)

TL;DR

This paper computes the stress-tensor correlator in 2+1 dimensional N=1 SYM theory using supersymmetric discrete light-cone quantization, revealing behavior consistent with conformal theory at small distances and BPS state dominance at large distances, with a critical coupling dependent on resolution.

Contribution

It introduces a numerical method for calculating stress-tensor correlators in supersymmetric theories that preserves supersymmetry at all approximation levels.

Findings

Correlator behaves as 1/r^6 at small r, matching conformal field theory predictions.

Large-r correlator dominated by BPS states, vanishing at a critical coupling.

Critical coupling increases linearly with the square root of transverse momentum resolution.

Abstract

Recent advances in string theory have highlighted the need for reliable numerical methods to calculate correlators at strong coupling in supersymmetric theories. We present a calculation of the correlator <0|T^{++}(r)T^{++}(0)|0> in N=1 SYM theory in 2+1 dimensions. The numerical method we use is supersymmetric discrete light-cone quantization (SDLCQ), which preserves the supersymmetry at every order of the approximation and treats fermions and bosons on the same footing. This calculation is done at large $N_c$. For small and intermediate r the correlator converges rapidly for all couplings. At small r the correlator behaves like 1/r^6, as expected from conformal field theory. At large r the correlator is dominated by the BPS states of the theory. There is, however, a critical value of the coupling where the large-r correlator goes to zero, suggesting that the large-r correlator can only be trusted to some finite coupling which depends on the transverse resolution. We find that this critical coupling grows linearly with the square root of the transverse momentum resolution.