arXiv subjects

V. P. Nair

Publications and source records attributed to V. P. Nair.

At least 73 records · Page 4Linked to original sources

arXiv2010

On the Casimir interaction between holes

We study the leading long-distance attractive force between two holes in a plate arising from a scalar field with Dirichlet boundary conditions on the plate. We use a formalism in which the interaction is governed by a non-local field theory which lives on the two holes. The interaction energy is proportional to Q_1 Q_2/r^7 at large separation r, where Q_1 and Q_2 are certain charges associated with the holes. We compute these charges for round and rectangular holes. We show that the 1/r^7 behavior is universal for separations large compared to the linear dimensions of the holes, irrespective of the spin or interactions of the bosonic field. We also study the interaction between two long thin slits, for which the energy falls off as 1/r^6.

hep-th↗

arXiv2010

A Note on Schwinger Mechanism and a Nonabelian Instability in a Nonabelian Plasma

We point out that there is a nonabelian instability for a nonabelian plasma which does not allow both for a net nonzero color charge and the existence of field configurations which are coherent over a volume $v$ whose size is determined by the chemical potential. The basic process which leads to this result is the Schwinger decay of chromoelectric fields, for the case where the field arises from commutators of constant potentials, rather than as the curl of spacetime dependent potentials. In terms of the fields, instability is obtained when Tr(DF)^2 > 0.

hep-th↗

arXiv2009

Massive Spin-2 fields of Geometric Origin in Curved Spacetimes

We study the consistency of a model which includes torsion as well as the metric as dynamical fields and has massive spin-2 particle in its spectrum. The massive spin-2 mode resides in the torsion, rather than in the metric. It is known that this model is tachyon- and ghost-free in Minkowski background. We show that this property remains valid and no other pathologies emerge in de Sitter and anti-de Sitter backgrounds, with some of our results extending to arbirary Einstein space backgrounds. This suggests that the model is consistent, at least at the classical level, unlike, e.g., the Fierz--Pauli theory.

hep-th↗

arXiv2009

The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections to String Tension

Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about -0.3% to -2.8% compared to the lowest order value. This is in good agreement with lattice estimates.

hep-th↗

arXiv2009

The Hamiltonian Approach to Yang-Mills (2+1): An Expansion Scheme and Corrections to String Tension

We carry out further analysis of the Hamiltonian approach to Yang-Mills theory in 2+1 dimensions which helps to place the calculation of the vacuum wave function and the string tension in the context of a systematic expansion scheme. The solution of the Schrodinger equation is carried out recursively. The computation of correlators is re-expressed in terms of a two-dimensional chiral boson theory. The effective action for this theory is calculated to first order in our expansion scheme and to the fourth order in a kinematic expansion parameter. The resulting corrections to the string tension are shown to be very small, in the range -0.3% to -2.8%, moving our prediction closer to the recent lattice estimates.

hep-th↗

arXiv2008

The Hamiltonian Analysis for Yang-Mills Theory on $R\times S^2$

Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified to a plane.

hep-th↗

arXiv2007

A Note on Graviton Amplitudes for New Twistor String Theories

A new class of twistor string theories were recently constructed by Abou-Zeid, Hull and Mason. The most interesting one of these theories has the particle content of N=8 supergravity. Arguments are given for the vanishing of the (+ - -)-helicity amplitude for gravitons which suggest that this theory describes a chiral N=8 supergravity rather than Einstein supergravity.

hep-th↗

arXiv2007

Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects

We explore further the Hamiltonian formulation of Yang-Mills theory in 2+1 dimensions in terms of gauge-invariant matrix variables. Coupling to scalar matter fields is discussed in terms of gauge-invariant fields. We analyze how the screening of adjoint (and other screenable) representations can arise in this formalism. A Schrodinger equation is then derived for the gluelump states which are the daughter states when an adjoint string breaks. A variational solution of this Schrodinger equation leads to an analytic estimate of the string-breaking energy which is within 8.8% of the latest lattice estimates.

hep-th↗

arXiv2007

The robustness of the vacuum wave function and other matters for Yang-Mills theory

In the first part of this paper, we present a set of simple arguments to show that the two-dimensional gauge anomaly and the (2+1)-dimensional Lorentz symmetry determine the leading Gaussian term in the vacuum wave function of (2+1)-dimensional Yang-Mills theory. This is to highlight the robustness of the wave function and its relative insensitivity to the choice of regularizations. We then comment on the correspondence with the explicit calculations done in earlier papers. We also make some comments on the nature of the gauge-invariant configuration space for Euclidean three-dimensional gauge fields (relevant to (3+1)-dimensional Yang-Mills theory).

hep-th↗

arXiv2006

Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry

We give a brief review of quantum Hall effect in higher dimensions and its relation to fuzzy spaces. For a quantum Hall system, the lowest Landau level dynamics is given by a one-dimensional matrix action whose large $N$ limit produces an effective action describing the gauge interactions of a higher dimensional quantum Hall droplet. The bulk action is a Chern-Simons type term whose anomaly is exactly cancelled by the boundary action given in terms of a chiral, gauged Wess-Zumino-Witten theory suitably generalized to higher dimensions. We argue that the gauge fields in the Chern-Simons action can be understood as parametrizing the different ways in which the large $N$ limit of the matrix theory is taken. The possible relevance of these ideas to fuzzy gravity is explained. Other applications are also briefly discussed.

hep-th↗

arXiv2006

The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory

We consider different large ${\cal N}$ limits of the one-dimensional Chern-Simons action $i\int dt~ \Tr (\del_0 +A_0)$ where $A_0$ is an ${\cal N}\times{\cal N}$ antihermitian matrix. The Hilbert space on which $A_0$ acts as a linear transformation is taken as the quantization of a $2k$-dimensional phase space ${\cal M}$ with different gauge field backgrounds. For slowly varying fields, the large ${\cal N}$ limit of the one-dimensional CS action is equal to the $(2k+1)$-dimensional CS theory on ${\cal M}\times {\bf R}$. Different large ${\cal N}$ limits are parametrized by the gauge fields and the dimension $2k$. The result is related to the bulk action for quantum Hall droplets in higher dimensions. Since the isometries of ${\cal M}$ are gauged, this has implications for gravity on fuzzy spaces. This is also briefly discussed.

hep-th↗

arXiv2006

The Chern-Simons One-form and Gravity on a Fuzzy Space

The one-dimensional ${\cal N}\times {\cal N}$-matrix Chern-Simons action is given, for large ${\cal N}$ and for slowly varying fields, by the $(2k+1)$-dimensional Chern-Simons action $S_{CS}$, where the gauge fields in $S_{CS}$ parametrize the different ways in which the large ${\cal N}$ limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite ${\cal N}$ and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold.

hep-th↗

arXiv2006

Color Skyrmions in the Quark-Gluon Plasma

We consider the general formulation of nonabelian fluid dynamics based on symmetry considerations. We point out that, quite generally, this admits solitonic excitations which are the color analog of skyrmions. Some general properties of the solitons are discussed.

hep-ph↗

arXiv2005

Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes

These lectures fall into two distinct, although tenouously related, parts. The first part is about fuzzy and noncommutative spaces, and particle mechanics on such spaces, in other words, noncommutative mechanics. The second part is a discussion/review of twistors and how they can be used in the calculation of Yang-Mills amplitudes. The point of connection between these two topics, discussed in the last section, is in the realization of holomorphic maps as the lowest Landau level wave functions, or as wave functions of the Hilbert space used for the fuzzy version of the two-sphere. This article is based on lectures presented at the conference on Higher Dimensional Quantum Hall Effect and Noncommutative Geometry, Trieste, March 2005, Winter School on Modern Trends in Supersymmetric Mechanics, Frascati, March 2005 and the Montreal-Rochester-Syracuse-Toronto Conference 2005, Utica, May 2005.

hep-th↗

arXiv2005

Nonsingular 4d-flat branes in six-dimensional supergravities

We show that six-dimensional supergravity models admit nonsingular solutions in the presence of flat three-brane sources with positive tensions. The models studied in this paper are nonlinear sigma models with the target spaces of the scalar fields being noncompact manifolds. For the particular solutions of the scalar field equations which we consider, only two brane sources are possible which are positioned at those points where the scalar field densities diverge, without creating a divergence in the Ricci scalar or the total energy. These solutions are locally invariant under 1/2 of D=6 supersymmetries, which, however, do not integrate to global Killing spinors. Other branes can be introduced by hand by allowing for local deficit angles in the transverse space without generating any kind of curvature singularities.

hep-th↗

arXiv2005

Multigluon amplitudes, ${\cal N}=4$ constraints and the WZW model

Classical ${\cal N}=4$ Yang-Mills theory is defined by the superspace constraints. We obtain a solution of a subset of these constraints and show that it leads to the maximally helicity violating (MHV) amplitudes. The action which leads to the solvable part of the constraints is a Wess-Zumino-Witten (WZW) action on a suitably extended superspace. The non-MHV tree amplitudes can also be expressed in terms of this action.

hep-th↗

arXiv2005

A Note on MHV Amplitudes for Gravitons

We show how the maximally helicity violating (MHV) scattering amplitudes for gravitons can be related to current correlators and vertex operators in twistor space. This is similar to what happens in Yang-Mills theory and raises the possibility of a direct twistor-string-like construction for ${\cal N}=8$ supergravity.

hep-th↗

arXiv2004

Edge States for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of abelian and nonabelian background magnetic fields. Carrying out an analysis similar to what was done for abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess-Zumino-Witten (WZW) theory generalized to higher dimensions.

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