Abstract
In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that within a chiral superspace $(x^+,\th)$, a two-dimensional field theory with two translational invariance and a chiral scaling symmetry can have enhanced local symmetry, under the assumption that the dilation spectrum is discrete and non-negative. Similar to the pure bosonic case, there are two kinds of minimal models, one being $N=(1,0)$ supersymmetric conformal field theories, while the other being $N=1$ supersymmetric warped conformal field theories (SWCFT). We study the properties of SWCFT, including the representations of the algebra, the space of states and the correlation functions of the superprimaries.
Highlights
Symmetry plays an essential role in quantum field theories
The vacuum of the NS sector in SWCFT2 is invariant under the global group OSPð1j2Þ × Uð1Þ, which is generated by fL0; LÆ1; P0; GÆ12g
We studied the supersymmetric extension of the warped conformal field theory
Summary
Symmetry plays an essential role in quantum field theories. The theories with more symmetries could be better constrained, such that their dynamics might be investigated even nonperturbatively. Gravity is generated by an Virasoro-Kac-Moody algebra This leads to the conjecture that under the CSS boundary conditions, the AdS3 gravity could be dual to a holographic warped conformal field theory. This AdS3=WCFT correspondence has been studied in [14,16,20,21,22,23,24]. In the Appendix, we discuss the conserved currents in the superspace and show that we can consistently work in the N 1⁄4 ð1; 0Þ superspace
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