Title: On N = 1 partition functions without R-symmetry

Abstract

Here, we examine the dependence of four-dimensional Euclidean N = 1 partition functions on coupling constants. In particular, we focus on backgrounds without R-symmetry, which arise in the rigid limit of old minimal supergravity. Backgrounds preserving a single supercharge may be classified as having either trivial or SU(2) structure, with the former including S⁴. We show that, in the absence of additional symmetries, the partition function depends non-trivially on all couplings in the trivial structure case, and (anti)-holomorphically on couplings in the SU(2) structure case. In both cases, this allows for ambiguities in the form of finite counterterms, which in principle render the partition function unphysical. However, we argue that on dimensional grounds, ambiguities are restricted to finite powers in relevant couplings, and can therefore be kept under control. On the other hand, for backgrounds preserving supercharges of opposite chiralities, the partition function is completely independent of all couplings. In this case, the background admits an R-symmetry, and the partition function is physical, in agreement with the results obtained in the rigid limit of new minimal supergravity. Based on a systematic analysis of supersymmetric invariants, we also demonstrate that N = 1 localization is not possible for backgrounds without R-symmetry.

Authors:

Knodel, Gino ^[1]; Liu, James T. ^[1]; Zayas, Leopoldo A. Pando ^[1]

---

+ Show Author Affiliations

1. Univ. of Michigan, Ann Arbor, MI (United States). Michigan Center for Theoretical Physics

Publication Date:

Wed Mar 25 00:00:00 EDT 2015

Research Org.:

Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1454566

Grant/Contract Number:  

SC0007859

Resource Type:

Accepted Manuscript

Journal Name:

Journal of High Energy Physics (Online)

Additional Journal Information:

Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:

Springer Berlin

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Supersymmetric gauge theory; Supergravity Models