Abstract
We show that N=4 supersymmetric-Yang-Mills (SYM) theory on R×S^{3} with gauge group SU(N) is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with SU(1,1)×U(1) invariant interactions. In this limit, a single complex adjoint scalar field survives, and part of its interaction is obtained by exactly integrating out the gauge boson of the SYM theory. Taking into account normal ordering, the interactions match the one-loop dilatation operator of the SU(1,1) sector, establishing the consistency of the limit at the quantum level. We discover a tantalizing field-theoretic structure, corresponding to a (1+1)-dimensional complex chiral boson on a circle coupled to a nondynamical gauge field, both in the adjoint representation of SU(N). The successful construction of a lower-dimensional nonrelativistic field theory in the SU(1,1) near-BPS limit provides a proof of concept for other BPS bounds. These are expected to lead to richer field theories in nonrelativistic corners of N=4 SYM that include fermions, gauge fields, and supersymmetry and can provide a novel path towards understanding strongly coupled finite-N dynamics of gauge theories.
Highlights
The BPS bound considered in this Letter isE ≥ Q1 þ S1; ð1Þ where E is the energy, Q1 one of the R charges and S1 one of the angular momenta of N 1⁄4 4 SYM on a three sphere
We show that N 1⁄4 4 supersymmetric-Yang-Mills (SYM) theory on R × S3 with gauge group SUðNÞ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with SUð1; 1Þ × Uð1Þ invariant interactions
Introduction.—Through the AdS=CFT correspondence, type IIB string theory on an AdS5 × S5 background is conjectured to possess a dual description in terms of N 1⁄4 4 supersymmetric-Yang-Mills (SYM) theory with gauge group SUðNÞ and coupling g
Summary
E ≥ Q1 þ S1; ð1Þ where E is the energy, Q1 one of the R charges and S1 one of the angular momenta of N 1⁄4 4 SYM on a three sphere. That this type of limit, known as a Spin Matrix theory limit, reveals nontrivial dynamics close to BPS bounds was discovered and examined in [8]. In this Letter, we find the first clear evidence of a nonrelativistic field-theoretic structure emerging from the near-BPS limit associated with (1). We chose the specific bound (1) mainly to provide an accessible representative for a proof of concept. All major subtleties of the constructions are captured, 0031-9007=20=124(17)=171602(5)
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