Modular symmetry and zeros in magnetic compactifications

Abstract We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus T2 and toroidal orbifolds T2/ℤN (N = 2, 3, 4, 6) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem. The zeros in magnetic compactifications therefore play an important role, as investigated in a series of recent papers. Focusing on the zeros and their positions, we study what type of boundary conditions must be satisfied by the zero modes after the modular transformation. The consideration in this paper justifies that the boundary conditions are common before and after the modular transformation.

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CHIRAL ZERO MODES ON VORTEX-TYPE INTERSECTING HETEROTIC FIVE-BRANES

Modern Physics Letters A ◽

10.1142/s0217732312500721 ◽

2012 ◽

Vol 27 (12) ◽

pp. 1250072 ◽

Cited By ~ 1

Author(s):

MASAYA YATA

Keyword(s):

Dirac Equation ◽

Zero Mode ◽

The Other ◽

Two Dimensional ◽

Complete Spectrum ◽

Type Solution ◽

Heterotic String Theory ◽

Zero Modes ◽

Brane Solution ◽

Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8×E8 heterotic string theory to search for localized chiral zero modes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zero modes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zero modes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zero mode localized on the heterotic five-brane system.

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CORRELATION FUNCTIONS AND ZERO MODES ON HIGHER GENUS RIEMANN SURFACES

International Journal of Modern Physics A ◽

10.1142/s0217751x88000369 ◽

1988 ◽

Vol 03 (04) ◽

pp. 841-860 ◽

Cited By ~ 22

Author(s):

M. BONINI ◽

R. IENGO

Keyword(s):

Scattering Amplitudes ◽

String Theory ◽

Correlation Functions ◽

Riemann Surfaces ◽

Covariant Formulation ◽

Two Dimensional ◽

Zero Modes ◽

Modular Transformation ◽

Higher Genus

We describe systematically the propagators and the zero modes of the various two dimensional fields which appear in the construction of the scattering amplitudes in the string theory, within the framework of the covariant formulation, and we discuss also their modular transformation properties.

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CONTINUUM AND LATTICE OVERLAP FOR CHIRAL FERMIONS ON THE TORUS

International Journal of Modern Physics A ◽

10.1142/s0217751x96001875 ◽

1996 ◽

Vol 11 (21) ◽

pp. 3987-4003 ◽

Cited By ~ 2

Author(s):

C.D. FOSCO

Keyword(s):

String Theory ◽

Boundary Conditions ◽

Effective Action ◽

Lattice Spacing ◽

Two Dimensional ◽

Dimensional Torus ◽

The Real ◽

Theory Result ◽

Twisted Boundary Conditions ◽

The Continuum

The overlap formulation is applied to calculate the chiral determinant on a two-dimensional torus with twisted boundary conditions. We first evaluate the continuum overlap, which is convergent and well-defined, and yields the correct string theory result for both the real and imaginary parts of the effective action. We then show that the lattice version of the overlap gives the continuum overlap results in the limit where the lattice spacing tends to zero, and that the subleading terms in that limit are irrelevant.

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DIRAC VARIABLES AND ZERO MODES OF GAUSS CONSTRAINT IN FINITE-VOLUME TWO-DIMENSIONAL QED

International Journal of Modern Physics A ◽

10.1142/s0217751x99001639 ◽

1999 ◽

Vol 14 (22) ◽

pp. 3531-3542 ◽

Cited By ~ 5

Author(s):

S. GOGILIDZE ◽

NEVENA ILIEVA ◽

V. N. PERVUSHIN

Keyword(s):

Finite Volume ◽

Ground State ◽

Zero Mode ◽

Collective Excitations ◽

Two Dimensional ◽

Massive Scalar ◽

Massive Scalar Field ◽

Gauge Transformations ◽

Zero Modes ◽

Nontrivial Topology

The finite-volume QED 1+1 is formulated in terms of Dirac variables by an explicit solution of the Gauss constraint with possible nontrivial boundary conditions taken into account. The intrinsic nontrivial topology of the gauge group is thus revealed together with its zero-mode residual dynamics. Topologically nontrivial gauge transformations generate collective excitations of the gauge field above Coleman's ground state, that are completely decoupled from local dynamics, the latter being equivalent to a free massive scalar field theory.

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Stability and instability results for the 2D [alpha]-Euler equations

10.32469/10355/62340 ◽

2017 ◽

Author(s):

◽

Shibi Kapisthalam Vasudevan

Keyword(s):

Steady State ◽

Euler Equations ◽

Nonlinear Term ◽

Zero Mode ◽

Two Dimensional ◽

Dimensional Torus ◽

Fourier Decomposition ◽

Inviscid Incompressible Fluid ◽

Stability And Instability ◽

Steady State Solutions

We study stability and instability of time independent solutions of the two dimensional a-Euler equations and Euler equations; the a-Euler equations are obtained by replacing the nonlinear term (u [times] [del.])u in the classical Euler equations of inviscid incompressible fluid by the term (v [times] [del.])u, where v is the regularized velocity satisfying (1 -[alpha]2[delta])v [equals] u, and [alpha] [greater than] 0. In the first part of the thesis, for the a-model, we develop analogues of the classical Arnol'd type stability criteria based on the energy-Casimir method for several settings including multi connected domains, periodic channels, and others. In the second part of the thesis, we study stability of a particular steady state, the unidirectional solution of the a-Euler equation on the two dimensional torus, having only one non zero mode in its Fourier decomposition. Using continued fractions, we give a proof of instability of the steady state under fairly general conditions. In the third part of the thesis we study various properties of a family of elliptic operators introduced by Zhiwu Lin in his work on instability of steady state solutions of the two dimensional Euler equations. This involves Birman-Schwinger type operators associated with the linearization of the Euler equations about the steady state and certain perturbation determinants.

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Spectral boundary conditions and index theorem for two-dimensional compact manifold with boundary

Annals of Physics ◽

10.1016/0003-4916(92)90085-z ◽

1992 ◽

Vol 218 (2) ◽

pp. 199-232 ◽

Cited By ~ 8

Author(s):

A.V Mishchenko ◽

Yu.A Sitenko

Keyword(s):

Boundary Conditions ◽

Compact Manifold ◽

Index Theorem ◽

Two Dimensional ◽

Manifold With Boundary

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FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND

Modern Physics Letters A ◽

10.1142/s0217732305018037 ◽

2005 ◽

Vol 20 (39) ◽

pp. 3045-3053 ◽

Cited By ~ 29

Author(s):

YONGQIANG WANG ◽

TIEYAN SI ◽

YUXIAO LIU ◽

YISHI DUAN

Keyword(s):

Phase Shift ◽

Zero Mode ◽

Two Dimensions ◽

Two Dimensional ◽

Yang Mills ◽

Zero Modes ◽

Extra Space ◽

Bohm Effect ◽

Aharonov Bohm ◽

Unified Description

We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present a unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study the localization of bulk fermions on a brane with the inclusion of Yang–Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov–Bohm effect.

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