Elliptic genus, anomaly cancellation and heterotic M-theory

Kang-Sin Choi,Soo-Jong Rey

doi:10.1103/physrevd.103.126001

Elliptic genus, anomaly cancellation and heterotic M-theory

Kang-Sin Choi, Soo-Jong Rey

Open Access

https://doi.org/10.1103/physrevd.103.126001

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Abstract

We derive global consistency condition for strongly coupled heterotic string in the presence of M5-branes. Its elliptic genus is interpretable as generating functional of anomaly polynomials and so, on anomaly-free vacua, the genus is both holomorphic and modular invariant. In the holomorphic basis, we identify the modular properties by calculating the phase. By interpreting the refinement parameters as background curvature of tangent and vector bundles, we show that the extended Bianchi identity for Kalb--Ramond field of heterotic M-theory is satisfied in the presence of arbitrary numbers of M5-branes.

Highlights

The anomaly of gauge and flavor symmetries played an important role as a unique window to physics at short distances, encompassing neutral pion decay, baryon number violation, matter contents of the Standard Model, quantum Hall edge states, topological insulators, and so on
At high-energy scale, the anomaly structure is embedded to global consistency condition of ultraviolet completion of string theory: modular invariance of closed strings and tadpole cancellation of open strings
We study global consistency condition of heterotic M-theory [1,2] or strongly coupled heterotic string theory [3], whose new feature is the presence of M5-branes in the M-theory bulk

Summary

INTRODUCTION

The anomaly of gauge and flavor symmetries played an important role as a unique window to physics at short distances, encompassing neutral pion decay, baryon number violation, matter contents of the Standard Model, quantum Hall edge states, topological insulators, and so on. At high-energy scale, the anomaly structure is embedded to global consistency condition of ultraviolet completion of string theory: modular invariance of closed strings and tadpole cancellation of open strings. These conditions, which lead to a specific form of anomalies, can be read off from the partition functions and their behavior in the complexified parameter plane. To identify consistent vacua in the presence of M5-branes, we may analyze the corresponding elliptic genera as a probe for anomaly cancellation Such elliptic genera are most elegantly computed by the topological vertex formalism [8,9]

ELLIPTIC GENUS

M5- AND M9-BRANES

ELLIPTIC GENUS FROM REFINED TOPOLOGICAL VERTEX

MODULAR ANOMALY AND HOLOMORPHIC ANOMALY

BIANCHI IDENTITY INCLUDING M5-BRANES