Vafa-Witten theorem on spontaneous breaking of parity

Einhorn, Martin B.; Wudka, José

doi:10.1103/physrevd.67.045004

Cited by 22 publications

(14 citation statements)

References 43 publications

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“…Let us make two remarks on this point. First, various loopholes in the original "proof" have been discussed in the literature [122][123][124][125][126][127][128], and therefore it cannot be regarded as an established mathematical theorem. Second, our result does not contradict recent work [128] on a Vafa-Witten-type theorem for fermion bilinears, since the positivity of the probability distribution function 63 The mass is given by the exponential decay of the correlation function, for which the multiplicative constant is irrelevant.…”

Section: C31 Two-color Qcd With Quark Massesmentioning

confidence: 99%

Singular values of the Dirac operator in dense QCD-like theories

Kanazawa

Wettig

Yamamoto

2011

J. High Energ. Phys.

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We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

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Section: C31 Two-color Qcd With Quark Massesmentioning

confidence: 99%

Singular values of the Dirac operator in dense QCD-like theories

Kanazawa

Wettig

Yamamoto

2011

J. High Energ. Phys.

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“…[17] for some explicit arguments, but also Ref. [18] for counterarguments). But even if it does apply, spontaneous CPviolation at finite temperature or baryon chemical potential (through meta-stable states) has been considered in the literature [19,20,21,22] and possible experimental signatures in heavy ion collisions have been put forward [23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

SpontaneousCPviolation in the strong interaction atθ=π

Boer

Boomsma

2008

Phys. Rev. D

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Spontaneous CP-violation in the strong interaction is analyzed at θ = π within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at θ = π depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. When available a comparison to earlier results from chiral perturbation theory is made. From our results we conclude that spontaneous CP-violation in the strong interaction is an inherently lowenergy phenomenon. In all cases we find agreement with the Vafa-Witten theorem, also at nonzero density and temperature. Meson masses and mixing in the CP-violating phase display some unusual features as a function of instanton interaction strength. A modification of the condition for charged pion condensation at nonzero isospin chemical potential and a novel phase of charged a0 mesons are discussed.

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“…(See also the studies for the scalar field by Einhorn and Larsen in Refs. [109,110] and by Marolf et al in Ref. [111].…”

Section: Discussionmentioning

confidence: 89%

Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops

Tanaka

Urakawa

2014

Progress of Theoretical and Experimental Physics

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It has been claimed that the super Hubble modes of the graviton generated during inflation can make loop corrections diverge. Even if we introduce an infrared (IR) cutoff at a comoving scale as an ad hoc but a practical way for the regularization, we encounter the secular growth, which may lead to the breakdown of perturbative expansion for a sufficiently long lasting inflation. In this paper, we show that the IR pathology concerning the graviton can be attributed to the presence of residual gauge degrees of freedom in the local observable universe as in the case of the adiabatic curvature perturbation. We will show that choosing the Euclidean vacuum as the initial state ensures the invariance under the above-mentioned residual gauge transformations. We will also show that as long as we consider a gauge invariant quantity in the local universe, we encounter neither the IR divergence nor the secular growth. The argument in this paper applies to general single field models of inflation up to a sufficiently high order in perturbation. * Electronic address: tanaka˙at˙yukawa.kyoto-u.ac.jp † Electronic address: yurakawa˙at˙ffn.ub.es

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Vafa-Witten theorem on spontaneous breaking of parity

Abstract: We revisit the proof provided by Vafa and Witten that there is no spontaneous parity breaking in theories with vector-like fermions. We argue that the various criticisms that have been leveled at the original proof do not invalidate it

Cited by 22 publications

References 43 publications

Singular values of the Dirac operator in dense QCD-like theories

Singular values of the Dirac operator in dense QCD-like theories

SpontaneousCPviolation in the strong interaction atθ=π

Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops

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