$\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $σ$-models

Abstract

A new symmetry of (1, 0) supersymmetric non-linear σ-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy W -symmetry of Howe and Papadopoulos associated with structure group reductions of the target space M. Our symmetry allows in particular non-trivial flux and instanton-like connections on vector bundles over M. We also investigate potential anomalies and show that cohomologically non-trivial terms in the quantum effective action are invariant under a corrected version of our symmetry. Consistency with heterotic supergravity at first order in α ′ is manifest and discussed.

Deformed Shatashvili-Vafa algebra for superstrings on AdS$_3\times {\cal M}_7$

“…Here the total N = 1 supercharge is simply G = G (N =2) + jψ, where j and ψ are 19 One could also consider using Type I R highest weight states with δ = 1 4k , but fusion rules are then not tractable. 20 In view of eq. (5.4) one possible explanation could be that the relevant algebra in that case is a more general algebra of the form SW( 3 2 , 3 2 , 2).…”

“…( 5.1), we did not find an obvious ansatz analogous to P in (2.5) that would generate SW k ( 3 2 , 3 2 , 2) in the world-sheet WZW description of AdS 3 × S 3 × S 3 × S 1 [34], although we have not ruled this out either. 20 More generally, one may analyse the backgrounds of the form [35,36]…”

“…The idea of the construction is to determine the chiral algebra that is generated 5 These identifications are motivated by semi-classical chiral symmetries, see [20,21].…”