[Paper Review] Low-energy structure of six-dimensional open-string vacua

Fabio Riccioni|ArXiv.org|Mar 18, 2002

Black Holes and Theoretical Physics2 references3 citations

TL;DR

This paper investigates the low-energy effective field theories of six-dimensional open-string vacua, focusing on (1,0) supergravity coupled to tensor, vector, and hypermultiplets. It establishes that anomalies—particularly gauge and supersymmetry anomalies—are canceled via a generalized Green-Schwarz mechanism, and that the resulting theory is fully determined by Wess-Zumino consistency conditions rather than supersymmetry, leaving a quartic gaugino coupling undetermined. This framework allows for consistent models with brane supersymmetry breaking, where local supersymmetry is non-linearly realized on certain branes.

ABSTRACT

This dissertation reviews some properties of the low-energy effective actions for six dimensional open-string models. The first chapter is a pedagogical introduction about supergravity theories. In the second chapter closed strings are analyzed, with particular emphasis on type IIB, whose orientifold projection, in order to build type-I models, is the subject of the third chapter. Original results are reported in chapters 4 and 5. In chapter 4 we describe the complete coupling of (1,0) six-dimensional supergravity to tensor, vector and hypermultiplets. The generalized Green-Schwarz mechanism implies that the resulting theory embodies factorized gauge and supersymmetry anomalies, to be disposed of by fermion loops. Consequently, the low-energy theory is determined by the Wess-Zumino consistency conditions, rather than by the requirement of supersymmetry, and this procedure does not fix a quartic coupling for the gauginos. In chapter 5 we describe the low-energy effective actions for type-I models with brane supersymmetry breaking, resulting form the simultaneous presence of supersymmetric bulks, with one or more gravitinos, and non-supersymmetric combinations of BPS branes.The consistency of the resulting gravitino couplings implies that local supersymmetry is non-linearly realized on some branes. We analyze in detail the ten-dimensional $USp(32)$ model and the six-dimensional (1,0) models.

Motivation & Objective

• To understand the low-energy effective field theory of six-dimensional open-string models, particularly those with minimal supersymmetry.
• To analyze the coupling of (1,0) six-dimensional supergravity to tensor, vector, and hypermultiplets, and determine the constraints on the resulting theory.
• To investigate the consistency of gravitino couplings in models with brane supersymmetry breaking, where bulk supersymmetry coexists with non-supersymmetric brane configurations.
• To clarify the role of Wess-Zumino consistency conditions in fixing the low-energy action when supersymmetry alone fails to do so.
• To examine the implications of non-linearly realized local supersymmetry on branes in the context of type-I models, including the $USp(32)$ and (1,0) models.

Proposed method

• The analysis begins with a pedagogical review of supergravity in various dimensions, focusing on ten- and eleven-dimensional theories as foundational frameworks.
• The paper derives the complete coupling of (1,0) six-dimensional supergravity to tensor, vector, and hypermultiplets using covariant field equations and anomaly consistency conditions.
• It applies the generalized Green-Schwarz mechanism to cancel gauge and supersymmetry anomalies, showing that these anomalies must be canceled by fermion loops.
• The Wess-Zumino consistency conditions are used as the primary constraint on the low-energy action, rather than supersymmetry, leading to a theory where the quartic gaugino coupling remains unfixed.
• For brane supersymmetry breaking models, the paper constructs consistent low-energy couplings by requiring consistency of gravitino interactions, leading to non-linearly realized local supersymmetry on the branes.
• The analysis includes detailed study of the ten-dimensional $USp(32)$ model and six-dimensional (1,0) models, using spinor algebra and Fierz identities in six dimensions to handle symplectic-Majorana spinors and bilinear contractions.

Experimental results

Research questions

• RQ1 How is the low-energy effective action of six-dimensional open-string vacua determined when supersymmetry does not fully fix the theory?
• RQ2 What role do Wess-Zumino consistency conditions play in constraining the effective action when anomalies are present?
• RQ3 How can gauge and supersymmetry anomalies be consistently canceled in (1,0) six-dimensional supergravity coupled to multiple multiplets?
• RQ4 What are the implications for the gravitino couplings when brane supersymmetry breaking occurs in a supersymmetric bulk?
• RQ5 In what way is local supersymmetry non-linearly realized on branes in models with mixed supersymmetric and non-supersymmetric brane sectors?

Key findings

• The low-energy effective theory of (1,0) six-dimensional supergravity coupled to tensor, vector, and hypermultiplets is not fully fixed by supersymmetry alone, due to the presence of undetermined quartic gaugino couplings.
• Anomalies—specifically factorized gauge and supersymmetry anomalies—are canceled via the generalized Green-Schwarz mechanism, requiring the presence of fermion loops.
• The Wess-Zumino consistency conditions are the primary constraint on the effective action, replacing supersymmetry as the determining principle, which leaves the quartic gaugino coupling unfixed.
• In models with brane supersymmetry breaking, consistent gravitino couplings require that local supersymmetry be non-linearly realized on the branes, even though the bulk remains supersymmetric.
• The ten-dimensional $USp(32)$ model and six-dimensional (1,0) models both exhibit consistent low-energy actions under these conditions, with non-linearly realized supersymmetry on the branes.
• The use of symplectic-Majorana spinors and Fierz identities in six dimensions ensures consistency of spinor bilinears and supports the derivation of anomaly cancellation and coupling constraints.