arXiv subjects

R. Parthasarathy

Publications and source records attributed to R. Parthasarathy.

43 records · Page 3Linked to original sources

arXiv1995

A Mechanism for Instanton Induced Chiral Symmetry Breaking in QCD

We propose a mechanism for instanton induced chiral symmetry breaking in QCD with fundamental scalars. The model Lagragian that we use has the same symmetry properties as QCD. The scalar fields develop vacuum expectation values at a non-trivial minimum and generate masses for thhe light quarks. The minimization condition is also used to break the $SU(N_f)$ flavour symmetry in order to make the $s$ quark heavier than the two lighter ones. Thus a vacuum of the theory that is not chirally invariant is obtained.

hep-ph↗

arXiv1994

Harmonic Gauss Maps and Self-Dual Equations in String Theory

The string world sheet, regarded as Riemann surface, in background $R^3$ and $R^4$ is described by the generalised Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean scalar curvature, we obtain an Abelian self-dual system, using $SO(3)$ and $SO(4)$ gauge fields constructed in our earlier studies. This compliments our earlier result that $h\surd g\ =\ 1$ surfaces exhibit Virasaro symmetry. The self-dual system so obtained is compared with self-dual Chern-Simons system and a generalized Liouville equation involving extrinsic geometry is obtained. \vspace{0.2cm} The world sheet in background $R^n, \ n>4$ is described by the generalized Gauss map. It is first shown that when the Gauss map is harmonic, the scalar mean curvature is constant. $SO(n)$ gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is shown that the harmonic map satisfies a non-Abelian self-dual system of equations for the gauge group $SO(2)\times SO(n-2)$.

hep-th↗

arXiv1994

A Conformal Field Theory of Extrinsic Geometry of 2-d Surfaces

In the description of the extrinsic geometry of the string world sheet regarded as a conformal immersion of a 2-d surface in $R^3$, it was previously shown that, restricting to surfaces with $h\surd{g}\ =\ 1$, where $h$ is the mean scalar curvature and $g$ is the determinant of the induced metric on the surface, leads to Virasaro symmetry. An explicit form of the effective action on such surfaces is constructed in this article which is the extrinsic curvature analog of the WZNW action. This action turns out to be the gauge invariant combination of the actions encountered in 2-d intrinsic gravity theory in light-cone gauge and the geometric action appearing in the quantization of the Virasaro group. This action, besides exhibiting Virasaro symmetry in $z$-sector, has $SL(2,C)$ conserved currents in the $\bar{z}$-sector. This allows us to quantize this theory in the $\bar{z}$-sector along the lines of the WZNW model. The quantum theory on $h\surd{g}\ =\ 1$ surfaces in $ R^3$ is shown to be in the same universality class as the intrinsic 2-d gravity theory.

hep-th↗

arXiv1994

QCD Strings as Constrained Grassmannian Sigma Model:

We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.

hep-lat↗

arXiv1993

Harmonic Maps and Self-Dual Equations for Immersed Surfaces

The immersion of the string world sheet, regarded as a Riemann surface, in $R^3$ and $R^4$ is described by the generalized Gauss map. When the Gauss map is harmonic or equivalently for surfaces of constant mean curvature, we obtain Hitchin's self-dual equations, by using $SO(3)$ and $SO(4)$ gauge fields constructed in our earlier studies. This complements our earlier result that $h\surd g\ =\ 1$ surfaces exhibit Virasaro symmetry. The self-dual system so obtained is compared with self-dual Chern-Simons system and a generalized Liouville equation involving extrinsic geometry is obtained. The immersion in $R^n, \ n>4$ is described by the generalized Gauss map. It is shown that when the Gauss map is harmonic, the mean curvature of the immersed surface is constant. $SO(n)$ gauge fields are constructed from the geometry of the surface and expressed in terms of the Gauss map. It is found Hitchin's self- duality relations for the gauge group $SO(2)\times SO(n-2)$.

hep-th↗

arXiv1993

Coherent States, Dynamics and Semiclassical Limit on Quantum Groups

Coherent states on the quantum group $SU_q(2)$ are defined by using harmonic analysis and representation theory of the algebra of functions on the quantum group. Semiclassical limit $q\rightarrow 1$ is discussed and the crucial role of special states on the quantum algebra in an investigation of the semiclassical limit is emphasized. An approach to $q$-deformation as a $q$-Weyl quantization and a relavence of contact geometry in this context is pointed out. Dynamics on the quantum group parametrized by a real time variable and corresponding to classical rotations is considered.

hep-th↗

arXiv1993

Extrinsic Curvature Induced 2-d Gravity

Abtract: 2-dimensional fermions are coupled to extrinsic geometry of a conformally immersed surface in ${\bf R}^3$ through gauge coupling. By integrating out the fermions, we obtain a WZNW action involving extrinsic curvature of the surface. Restricting the resulting effective action to surfaces of $h\sqrt g=1$, an explicit form of the action invariant under Virasaro symmetry is obtained. This action is a sum of the geometric action for the Virasaro group and the light-cone action of 2-d gravity plus an interaction term. The central charges of the theory in both the left and right sectors are calculated.

hep-th↗