Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions

Abstract

We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous Z_N x Z_N symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.

30 pages

References in corpus (16)

• Noncommutative Field Theory
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• Aspects of Gauge Theory on Commutative and Noncommutative Tori
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• Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories
• Quantum Aspects of GMS Solutions of Noncommutative Field Theory and Large N Limit of Matrix Models
• One-loop Noncommutative U(1) Gauge Theory from Bosonic Worldline Approach
• A Remark On Field Theories On The Non-Commutative Torus

Cited by in corpus (26)

• Gauge Threshold Corrections in Intersecting Brane World Models
• Large $N$ reduction with the Twisted Eguchi-Kawai model
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Vacuum Choices and the Predictions of Inflation
• Phase structure of twisted Eguchi-Kawai model
• Closed Strings Tachyons and Non-Commutative Instabilities
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• Holographic bounds on the UV cutoff scale in inflationary cosmology
• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• Open Wilson Lines and Group Theory of Noncommutative Yang-Mills Theory in Two Dimensions
• A graviton propagator for inflation
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Inflation as a probe of new physics
• Volume independence for Yang-Mills fields on the twisted torus
• On the relation between non-commutative field theories at theta = infinity and large N matrix field theories
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• The twisted gradient flow coupling at one loop
• The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus
• Renormalization on noncommutative torus
• KK-Masses in Dipole Deformed Field Theories
• Strong Coupling Phenomena on the Noncommutative Plane
• Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
• Center-vortex semiclassics with non-minimal 't Hooft fluxes on ${\mathbb{R}}^2\times T^2$ and center stabilization at large $N$
• Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
• Paired quantum Hall states on noncommutative two-tori
• A note on the center of mass in non-commutative theories