Supersymmetric Galilean Electrodynamics

We study the renormalization of an $$ \mathcal{N} $$ N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, the theory naturally flows toward the relativistic sigma model where Lorentz symmetry emerges. In the superspace formalism, we develop a heat kernel method that is covariantized with respect to the bimetric target-space geometry, using which we evaluate the one-loop beta-functions of the Lifshitz sigma model. This study forms an essential step toward a thorough understanding of the quantum critical supermembrane as a candidate high-energy completion of the relativistic supermembrane.

Renormalization of supersymmetric Lifshitz sigma models

Yan

2023

The Panorama of Spin Matrix theory

Baiguera

Harmark

Lei

2023

Spin Matrix theory describes near-BPS limits of $$ \mathcal{N} $$ N = 4 SYM theory, which enables us to probe finite N effects like D-branes and black hole physics. In previous works, we have developed the spherical reduction and spin chain methods to construct Spin Matrix theory for various limits. In this paper, by considering a supercharge $$ \mathcal{Q} $$ Q which is cubic in terms of the letters, we construct the Hamiltonian of the largest Spin Matrix theory of $$ \mathcal{N} $$ N = 4 SYM, called the PSU(1, 2|3) Spin Matrix theory, as $$ H=\left\{\mathcal{Q},{\mathcal{Q}}^{\dagger}\right\} $$ H = Q Q † . We show the resulting Hamiltonian is automatically positive definite and manifestly invariant under supersymmetry. The Hamiltonian is made of basic blocks which transform as supermultiplets. A novel feature of this Hamiltonian is its division into D-terms and F-terms that are separately invariant under PSU(1, 2|3) symmetry and positive definite. As all the other Spin Matrix theories arising from $$ \mathcal{N} $$ N = 4 SYM can be acquired by turning off certain letters in the theory, we consider our work as revealing the “Panorama” of Spin Matrix theory.

Non-relativistic intersecting branes, Newton-Cartan geometry and AdS/CFT

Lambert,

Smith

2024

We discuss non-relativistic variants of four-dimensional $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory obtained from generalised Newton-Cartan geometric limits of D3-branes in ten-dimensional spacetime. We argue that the natural interpretation of these limits is that they correspond to non-relativistic D1-branes or D3-branes intersecting the original D3-branes. The resulting gauge theories have dynamics that reduce to quantum mechanics on monopole moduli space or two-dimensional sigma-models on Hitchin moduli space respectively. We show that these theories possess interesting infinite-dimensional symmetries and we discuss the dual AdS geometries.