Speaker
Description
Supersymmetric localization is a powerful technique to get exact results from the path integral of a supersymmetric field theories defined on a compact manifold [1,2,3]. Localization relies on the definition of supersymmetric theories in curved space, which need to preserve part of the original supersymmetry existing in flat space. In the relativistic case, this problem was systematically addressed in the seminal work by Festuccia and Seiberg [4].
Motivated by recent progress in non-relativistic field theories, we study the analogous problem for supersymmetric theories coupled to Newton-Cartan geometry [5]. In particular, preserving supersymmetry in a four-dimensional Lorentzian theory with R-symmetry is equivalent to the existence of a conformal null Killing vector in the background geometry [6, 7]. This condition is naturally realized on three-dimensional manifolds obtained via null-reduction [8] of a pseudo-Riemannian geometry.
In this work, I show that, among other solutions, torsional Newton–Cartan geometries provide consistent curved backgrounds on which supersymmetry is preserved. I further show that super-Galilean theories, including super-Galilean Yang–Mills, as well as a non-relativistic chiral theory – both obtained via null reduction of their four-dimensional relativistic counterparts – can be consistently coupled to these curved backgrounds and are Q–exact, i.e. they can be written as supersymmetric variations of scalar quantities. Finally, I comment on the realization of supersymmetric localization in this context.
[1] V. Pestun, Commun.Math.Phys. 313 (2012) 71-129.
[2] B. Willett, DOI: 10.1088/1751-8121/aa612f.
[3] A. Kapustin, B. Willett, I. Yaakov, JHEP 1003:089,2010.
[4] G. Festuccia, N. Seiberg, JHEP 1106:114,2011.
[5] J. Hartong, N. A. Obers, G. Oling, DOI: 10.3389/fphy.2023.1116888.
[6] C. Klare, A. Tomasiello, A. Zaffaroni, DOI: 10.1007/jhep08(2012)061.
[7] D. Cassani, C. Klare, D. Martelli, A. Tomasiello, A. Zaffaroni, Commun.Math.Phys. 327 (2014) 577-602.
[8] C. Duval, G. Burdet, H. P. K¨unzle, M. Perrin; Phys. Rev. D31, 1841.