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Rajamani Narayanan

Publications and source records attributed to Rajamani Narayanan.

At least 73 records · Page 4Linked to original sources
arXiv1999

Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator

We investigate the approach to the continuum limit of the spectrum of the Hermitian Wilson-Dirac operator in the supercritical mass region for pure gauge SU(2) and SU(3) backgrounds. For this we study the spectral flow of the Hermitian Wilson-Dirac operator in the range $0\le m\le 2$. We find that the spectrum has a gap for $0 < m \le m_1$ and that the spectral density at zero, $ρ(0;m)$, is non-zero for $m_1\le m\le 2$. We find that $m_1\to 0$ and, for $m \ne 0, ρ(0;m)\to 0$ (exponential in the lattice spacing) as one goes to the continuum limit. We also compute the topological susceptibility and the size distribution of the zero modes. The topological susceptibility scales well in the lattice spacing for both SU(2) and SU(3). The size distribution of the zero modes does not appear to show a peak at a physical scale.

hep-lat↗
arXiv1998

A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator

We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes and simplify our numerical computations. Details concerning the numerical implementation of the Overlap-Dirac operator are presented.

hep-lat↗
arXiv1998

Topological Susceptibility and Zero Mode Size in Lattice QCD

We use the overlap formalism to define a topological index on the lattice. We study the spectral flow of the hermitian Wilson-Dirac operator and identify zero crossings with topological objects. We determine the topological susceptibility and zero mode size distribution, and we comment on the stability of our results.

hep-lat↗
arXiv1998

Evidence for fractional topological charge in SU(2) pure Yang-Mills theory

We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge field configurations where the index of the hermitian Wilson-Dirac operator in the adjoint representation is not four times the index in the fundamental representation. This could imply a topological basis for the existence of degenerate vacua in supersymmetric Yang-Mills theories.

hep-lat↗
arXiv1998

Spectral flow, condensate and topology in lattice QCD

We study the spectral flow of the Wilson-Dirac operator H(m) with and without an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice gauge field ensembles in the range $0\le m \le 2$. We have used ensembles generated from the Wilson gauge action, an improved gauge action, and several two-flavor dynamical quark ensembles. Two regions in $m$ provide a generic characterization of the spectrum. In region I defined by $m\le m_1$, the spectrum has a gap. In region II defined by $m_1\le m \le 2$, the gap is closed. The level crossings in H(m) that occur in region II correspond to localized eigenmodes and the localization size decreases monotonically with the crossing point down to a size of about one lattice spacing. These small modes are unphysical, and we find the topological susceptibility is relatively stable in the part of region II where the small modes cross. We argue that the lack of a gap in region II is expected to persist in the infinite volume limit at any gauge coupling. The presence of a gap is important for the implementation of domain wall fermions.

hep-lat↗
arXiv1998

A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions

We study three practical implementations of the Overlap-Dirac operator $D_o= (1/2) [1 + γ_5ε(H_w)]$ in four dimensions. Two implementations are based on different representations of $ε(H_w)$ as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing $ε(H_w)$ using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator $H_o=γ_5 D_o$, we study its spectrum in a smooth SU(2) instanton background with the aim of comparing the three implementations of $D_o$. We also present some results in SU(2) gauge field backgrounds generated at $β=2.5$ on an $8^4$ lattice. Chiral properties have been numerically verified.

hep-lat↗
arXiv1998

Evidence for fractional topological charge in SU(2) pure Yang-Mills theory

We investigate the spectral flows of the hermitian Wilson-Dirac operator in the fundamental and adjoint representations on two ensembles of pure SU(2) gauge field configurations at the same physical volume. We find several background gauge field configurations where the index of the hermitian Wilson-Dirac operator in the adjoint representation is not four times the index in the fundamental representation. This could imply a topological basis for the gluino condensate in supersymmetric Yang-Mills theories.

hep-lat↗
arXiv1998

Ginsparg-Wilson relation and the overlap formula

The fermionic determinant of a lattice Dirac operator that obeys the Ginsparg-Wilson relation factorizes into two factors that are complex conjugate of each other. Each factor is naturally associated with a single chiral fermion and can be realized as a overlap of two many body vacua.

hep-lat↗
arXiv1998

Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions

We study the spectrum of $H(m)=γ_5 W(-m)$ with $W(m)$ being the Wilson-Dirac operator on the lattice with bare mass equal to $m$. The background gauge fields are generated using the SU(3) Wilson action at $β=5.7$ on an $8^3\times 16$ lattice. We find evidence that the spectrum of $H(m)$ is gapless for $1.02 < m < 2.0$, implying that the physical quark is massless in this whole region.

hep-lat↗
arXiv1998

The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds

We study the spectral flow of the hermitian Wilson-Dirac operator $\ham(m)$ as a function of $m$ in smooth SU(2) instanton backgrounds on the lattice. For a single instanton background with Dirichlet boundary conditions on $\ham(m)$, we find a level crossing in the spectral flow of $\ham(m)$, and we find the shape of the crossing mode at the crossing point to be in good agreement with the zero mode associated with the single instanton background. With anti-periodic boundary conditions on $\ham(m)$, we find that the instanton background in the singular gauge has the correct spectral flow but the one in regular gauge does not. We also investigate the spectral flows of two instanton and instanton-anti-instanton backgrounds.

hep-lat↗
arXiv1997

The Overlap Formalism and Topological Susceptibility on the Lattice

Recent lattice measurements of the topological susceptibility of SU(2) gauge theory using improved cooling and inverse-blocking are in disagreement. We use the overlap method, which probes the fermionic sector of the theory directly, to help resolve this discrepancy.

hep-lat↗
arXiv1997

Parity Invariant Lattice Regularization of Three-Dimensional Gauge-Fermion System

In three dimensions, the effective action for the gauge field induced by integrating out a massless Dirac fermion is known to give either a parity-invariant or a parity-violating result, depending on the regularization scheme. We construct a lattice formulation of the massless Dirac fermion using the overlap formalism. We show that the result is parity invariant in contrast to the formulation using Wilson fermions in the massless limit. This facilitates a non-perturbative study of three-dimensional massless Dirac fermions interacting with a gauge field in a parity invariant setting with no need for fine-tuning.

hep-th↗
arXiv1997

Chiral Gauge Theories in the Overlap Formalism

The overlap formula for the chiral determinant is presented and the realization of gauge anomalies and gauge field toplogy in this context is discussed. The ability of the overlap formalism to deal with supersymmetric theories and Majorana-Weyl fermions is outlined. Two applications of the overlap formalism are discussed in some detail. One application is the computation of a fermion number violating process in a two dimensional U(1) chiral gauge theory. The second application is a measurement of the probability ditribution of the index of the chiral Dirac operator in four dimensional pure SU(2) lattice gauge theory.

hep-lat↗
arXiv1997

Monte Carlo evaluation of a fermion number violating observable in 2D

We describe in some detail a computer evaluation of a 't Hooft vertex in a two dimensional model using the overlap. The computer result agrees with the known exact continuum value, and in this sense our work is a first successful fully dynamical simulation of a chiral gauge theory on the lattice. We add some new data to numbers obtained earlier and provide a selfcontained description which should make it easy for others to reproduce and follow up on our work.

hep-lat↗
arXiv1997

A numerical test of the continuum index theorem on the lattice

The overlap formalism of chiral fermions provides a tool to measure the index, Q, of the chiral Dirac operator in a fixed gauge field background on the lattice. This enables a numerical measurement of the probability distribution, p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure SU(2) gauge theory by measuring Q on 140 independent gauge field configurations generated on a 12^4 lattice using the standard single plaquette Wilson action at a coupling of beta=2.4. This distribution is in good agreement with a recent measurement [8] of the distribution of the topological charge on the same lattice using the same coupling and the same lattice gauge action. In particular we find =3.3(4) to be compared with = 3.9(5) found in [8]. The good agreement between the two distributions is an indication that the continuum index theorem can be carried over in a probabilistic sense on to the lattice.

hep-lat↗