$$ \mathcal{G} $$-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.

$$ \mathcal{SW}\left(\frac{3}{2},2\right) $$ subsymmetry in G2, Spin(7) and $$ \mathcal{N} $$ = 2 CFTs

“…5 They admit a 2-form -the Kähler form -covariantly constant under a connection -Levi-Civita -with holonomy contained in U(n). Perturbatively at least, this yields a worldsheet U(1) chiral symmetry with current J 3 [26]; see also [27]. Vir N =2 c is an extension of the N = 1 superconformal algebra (2.1)-(2.3) by this current J 3 and its partner G 3 , which is a supersymmetry current.…”

Deformed Shatashvili-Vafa algebra for superstrings on AdS3 × ℳ7

“…(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]…”

“…In order for this to lead to a critical string background, the level of the sl(2, R)(1) k algebra, describing the AdS3 factor, is also k; this level is related to the AdS3 radius R AdS as k = R 2 AdS /α 5. These identifications are motivated by semi-classical chiral symmetries, see[20,21].…”

“…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.…”

New G2-conifolds in M-theory and their field theory interpretation

“…Advances have been made both from the physics [9][10][11][12][13][14] and the mathematics [1,[15][16][17][18][19][20][21], and involves aspects such as a string-worldsheet interpretation [22][23][24], a better understanding of exceptional gauge bundles and instantons [25][26][27][28][29][30][31], in addition to non-perturbative aspects such as M 2 instantons and their relation to exceptional enumerative geometry [32][33][34].…”