Gauge freedom in chiral gauge theory with vacuum overlap

Kikukawa, Yoshio

doi:10.1016/s0920-5632(97)00840-2

Nuclear Physics B - Proceedings Supplements

1998

DOI: 10.1016/s0920-5632(97)00840-2

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Gauge freedom in chiral gauge theory with vacuum overlap

Yoshio Kikukawa

Abstract: Dynamical nature of the gauge degrees of freedom and its effect to fermion spectrum are studied at β = ∞ for two-and four-dimensional nonabelian chiral gauge theories in the vacuum overlap formalism. It is argued that the disordered gauge degrees of freedom does not contradict to the chiral spectrum of lattice fermion.

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2000

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Global obstructions to gauge-invariance in chiral gauge theory on the lattice

Adams¹

2000

Nuclear Physics B

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It is shown that certain global obstructions to gauge-invariance in chiral gauge theory, described in the continuum by Alvarez-Gaumé and Ginsparg, are exactly reproduced on the lattice in the Overlap formulation at small non-zero lattice spacing (i.e. close to the classical continuum limit). As a consequence, the continuum anomaly cancellation condition d abc R = 0 is seen to be a necessary (although not necessarily sufficient) condition for anomaly cancellation on the lattice in the Overlap formulation. 8 The viability of this approach has been a topic of debate in the literature [16,17,18], although there is a body of evidence which is supportive of it -see, e.g., [19,20]. 9 The formulation of ref.'s [13, 14] (a functional integral formulation based on a lattice Dirac operator satisfying the Ginsparg-Wilson relation [21], which had been rediscovered outside of the overlap setting in the work of Hasenfratz and collaborators [22, 23]) is structurally identical to the overlap formulation after identifying the chiral fermion measures in the functional integral with the many-body groundstates in the overlap. More on this in §2, where the many-body groundstates are the "unit volume elements" in our terminology. 10 The argument in [13] relied on a result on the structure of the abelian axial anomaly [24], which has been further elucidated in [25]. 5

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Global obstructions to gauge-invariance in chiral gauge theory on the lattice

Adams¹

2000

Nuclear Physics B

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Gauge freedom in chiral gauge theory with vacuum overlap

Cited by 1 publication

References 49 publications

Global obstructions to gauge-invariance in chiral gauge theory on the lattice

Global obstructions to gauge-invariance in chiral gauge theory on the lattice

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