Generalized mirror symmetry and trace anomalies

TL;DR

This paper introduces a generalized mirror symmetry in M-theory compactifications on X7, linking Betti numbers and analyzing trace anomalies, with implications for supergravity theories with various supersymmetries.

Contribution

It defines a new generalized mirror symmetry involving Betti numbers and explores its impact on trace anomalies in supergravity theories.

Findings

Generalized mirror symmetry flips the sign of rho.

Self-mirror theories with rho=0 have vanishing trace anomaly.

Examples include supergravity theories with N ≥ 4 and N ≤ 4.

Abstract

We consider compactification of M-theory on X7 with betti numbers (b_0, b_1, b_2, b_3, b_3, b_2, b_1, b_0) and define a generalized mirror symmetry (b_0, b_1, b_2, b_3) goes to (b_0, b_1, b_2 -rho/2, b_3+rho/2)$ under which rho = 7b_0-5b_1+3b_2 -b_3 changes sign. Generalized self-mirror theories with rho=0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with N \geq 4 and supergravity plus matter with N \leq 4.