Minos Axenides

The Level crossing phenomenon with Yukawa interactions

Abstract In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean Dirac operator in three, four and five dimensions (D) in the presence of topologically non-trivial external fields. More specifically we study the cases of the instanton (D = 4), sphaleron (D = 3) as well as that of the (D = 5) Dirac operator that pertains to the existence of the global SU(2) anomaly. We establish the existence of normalizable massive fermion zero modes in all three cases. We give closed form expressions which relate the massive with the massless zero modes. As a consequence the level crossing phenomenon is shown to be manifest and generic in the presence of Yukawa interactions.

ON SPHALERON DEFORMATIONS INDUCED BY YUKAWA INTERACTIONS

Due to the presence of the chiral anomaly sphalerons, half a number of Chern-Simons (CS=1/2) are the only static configurations that allow a fermion level crossing in the two-dimensional Abelian-Higgs model with massless fermions, i.e. in the absence of Yukawa interactions. In the presence of fermion-Higgs interactions we demonstrate the existence of zero energy solutions to the one-dimensional Dirac equation at deformed sphalerons with CS ≠ 1/2. Induced level crossing due to Yukawa interactions illustrates a non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the equivalence between parity anomaly in odd and chiral anomaly in even dimensions. We discuss a subtle manifestation of this effect in the standard electroweak theory at finite temperatures.Due to the presence of the chiral anomaly sphalerons with Chern-Simons number a half (CS=1/2) are the only static configurations that allow for a fermion level crossing in the two-dimensional Abelian-Higgs model with massless fermions, i.e. in the absence of Yukawa interactions. In the presence of fermion-Higgs interactions we demonstrate the existence of zero energy solutions to the one-dimensional Dirac equation at deformed sphalerons with CS

A Z2 structure in the configuration space of Yang–Mills theories

neq 1/2 .

CHARGED COSMIC STRING NUCLEATION IN DE SITTER SPACE

Induced level crossing due to Yukawa interactions illustrates a non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the equivalence between parity anomaly in odd and the chiral anomaly in even dimensions. We discuss a subtle manifestation of this effect in the standard electroweak theory at finite temperatures.

Cosmic string nucleation near the inflationary phase boundary

We argue for the presence of a Z2 topological structure in the space of static gauge–Higgs field configurations of SU(2n) and SO(2n) Yang–Mills theories. We rigorously prove the existence of a Z2 homotopy group of mappings from the two‐dimensional projective sphere RP2 into SU(2n)/Z2 and SO(2n)/Z2 Lie groups, respectively. Consequently the symmetric phase of these theories admits infinite surfaces of odd‐parity static and unstable gauge field configurations which divide into two disconnected sectors with integer Chern–Simons numbers n and n+1/2, respectively. Such a Z2 structure persists in the Higgs phase of the above theories and accounts for the existence of CS=1/2 odd‐parity saddle point solutions to the field equations which correspond to spontaneous symmetry breaking mass scales.

TOPOLOGICAL CLASSIFICATION OF ODD-PARITY SPHALERON DEFORMATIONS

We investigate aspects of the nucleation of charged circular cosmic strings in de Sitter space. By including the self-gravity for a single circular string loop we obtain the classical potential energy barrier and compute the quantum mechanical tunneling probability to horizon sizes in the semiclassical approximation. We also discuss the classical evolution of a pair of oppositely charged circular strings after their nucleation.

On string tunneling in power law inflationary universes

Abstract We investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.

AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

We discuss topological aspects of the electroweak sphaleron and its odd-parity deformations. We demonstrate that they are uniquely classified in terms of their odd or even-parity pure gauge field behavior at spatial infinity. Fermion level crossing occurs only for odd-parity configurations, which are topologically disconnected from the vacuum. They contribute to the high temperature unsuppressed baryon violating thermal transitions. Deformations with even-parity pure gauge behavior at spatial infinity are topologically trivial and do not mediate baryon number violation in the early universe.

THE SU(2) GLOBAL ANOMALY THROUGH LEVEL CIRCLING

Abstract We consider the evolution of circular string loops in power law expanding universes represented by a spatially flat Friedman-Robertson-Walker metric with scale factor a(t) ∝ tp, where t is the cosmic time and p ⩾ 0. Our main result is the existence of a “magic” power p m = 3 + 2 2 . In spacetimes with p

The global SU (2) anomaly for massive fermions

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.