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R. Narayanan

Publications and source records attributed to R. Narayanan.

At least 37 records · Page 2Linked to original sources
arXiv2009

The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice

We consider the large N limit of four dimensional SU(N) Yang-Mills field coupled to adjoint fermions on a single site lattice. We use perturbative techniques to show that the Z^4_N center-symmetries are broken with naive fermions but they are not broken with overlap fermions. We use numerical techniques to support this result. Furthermore, we present evidence for a non-zero chiral condensate for one and two Majorana flavors at one value of the lattice gauge coupling.

hep-lat↗
arXiv2009

Two dimensional fermions in four dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\frac{1}{Λ_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.

hep-lat↗
arXiv2009

The vector meson mass in the large N limit of QCD

The vector meson mass is computed as a function of quark mass in the large N limit of QCD. We use continuum reduction and directly compute the vector meson propagator in momentum space. Quark momentum is inserted using the quenched momentum prescription.

hep-lat↗
arXiv2007

Universality of large N phase transitions in Wilson loop operators in two and three dimensions

The eigenvalue distribution of a Wilson loop operator of fixed shape undergoes a transition under scaling at infinite N. We derive a large N scaling function in a double scaling limit of the average characteristic polynomial associated with the Wilson loop operator in two dimensional QCD. We hypothesize that the transition in three and four dimensional large N QCD are also in the same universality class and provide a numerical test for our hypothesis in three dimensions.

hep-th↗
arXiv2007

A survey of large N continuum phase transitions

The main focus of this talk is the physics of large N QCD on a continuum torus. A cascade of phase transitions associated with the breaking of U(1) symmetries will be discussed. The continuum Wilson loop as a function of its area will be discussed along with its universality properties and the associated double scaling limit. Some recent progress in twisted Eguchi-Kawai is presented. Gauge field topology and $θ$ vacuua are also discussed in the context of large N gauge theories. Phase transitions in 2D large N principal chiral models are compared with similar transitions in large $N$ gauge theories. Finally, connections to some topics in string theory and gravity are briefly described.

hep-lat↗
arXiv2007

Universal properties of large N phase transitions in Wilson loops

Numerical studies support the conjecture that in continuum planar QCD the eigenvalue density of a Wilson loop operator undergoes a transition as the loop is dilated while keeping the loop shape fixed. A second part of the conjecture is that the transition obeys large N universality and that this universality class is the same in 2, 3 and 4 Euclidean space-time dimensions. The focus of the talk will be on clarifying precisely what the conjecture is claiming.

hep-lat↗
arXiv2007

Phases of three dimensional large N QCD on a continuum torus

It is established by numerical means that continuum large N QCD defined on a three dimensional torus can exist in four different phases. They are (i) confined phase; (ii) deconfined phase; (iii) small box at zero temperature and (iv) small box at high temperatures.

hep-lat↗
arXiv2007

Boundary multifractality in critical 1D systems with long-range hopping

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary.

cond-mat.mes-hall↗
arXiv2006

More about chiral symmetry restoration at finite temperature in the planar limit

In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge configuration by gauge configuration, have distributions described by a Gaussian Hermitian matrix model. However, combinations of eigenvalues that are scale and shift invariant only on the average, do not match this matrix model.

hep-lat↗
arXiv2006

Chiral symmetry restoration at finite temperature in the planar limit

We investigate numerically chiral symmetry restoration at finite temperature in the planar limit in the deconfined phase, both when it is stable and when the system is supercooled. We find chiral symmetry restoration at $T_χ= T_d$, where $T_d$ is the temperature of the deconfinement transition in pure gauge theory and $T_χ< T_d$ in the supercooled deconfined phase. In the stable case the spectrum of the Dirac operator opens a gap in a discontinuous manner and in the supercooled phase the gap seems to vanish continuously.

hep-th↗
arXiv2006

Infinite N phase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.

hep-th↗
arXiv2005

Large N reduction on a twisted torus

We consider SU(N) lattice gauge theory at infinite N defined on a torus with a CP invariant twist. Massless fermions are incorporated in an elegant way, while keeping them quenched. We present some numerical results which suggest that twisting can make numerical simulations of planar QCD more efficient.

hep-lat↗
arXiv2005

Griffiths phase in the thermal quantum Hall effect

Two dimensional disordered superconductors with broken spin-rotation and time-reversal invariance, e.g. with p_x+ip_y pairing, can exhibit plateaus in the thermal Hall coefficient (the thermal quantum Hall effect). Our numerical simulations show that the Hall insulating regions of the phase diagram can support a sub-phase where the quasiparticle density of states is divergent at zero energy, ρ(E)\sim |E|^{1/z-1}, with a non-universal exponent $z>1$, due to the effects of rare configurations of disorder (``Griffiths phase'').

cond-mat.mes-hall↗
arXiv2005

The quark mass dependence of the pion mass at infinite N

In planar QCD, in two space time dimensions, the meson eigenvalue equation has a nonlocal structure interpretable as resulting from hidden degrees of freedom. The nonlocality can be reconstructed from the functional form of the pion mass dependence on quark mass within an expansion starting from a special one dimensional Schroedinger problem. The one dimensional problem makes the pion mass depend on the quark mass through a simple quadratic relation which is shown to be compatible also with numerical data obtained in four dimensions.

hep-lat↗