arXiv subjects

T. R. Govindarajan

Publications and source records attributed to T. R. Govindarajan.

At least 37 records · Page 2Linked to original sources

arXiv2012

Topological stability of broken symmetry on fuzzy spheres

We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform configuration which diverge, due to Mermin-Wagner-Hohenberg-Coleman theorem, leading to the decay of the condensate. Interesting implications of enhanced topological stability of the configurations are pointed out.

hep-th↗

arXiv2012

Phase structure of fuzzy black holes

Noncommutative deformations of the BTZ blackholes are described by noncommutative cylinders. We study the scalar fields in this background. The spectrum is studied analytically and through numerical simulations we establish the existence of novel `stripe phases'. These are different from stripes on Moyal spaces and stable due to topological obstruction.

gr-qc↗

arXiv2011

Novel black hole bound states and entropy

We solve for the spectrum of the Laplacian as a Hamiltonian on $\mathbb{R}^{2}-\mathbb{D}$ and in $\mathbb{R}^{3}-\mathbb{B}$. A self-adjointness analysis with $\partial\mathbb{D}$ and $\partial\mathbb{B}$ as the boundary for the two cases shows that a general class of boundary conditions for which the Hamiltonian operator is essentially self-adjoint are of the mixed (Robin) type. With this class of boundary conditions we obtain "bound state" solutions for the Schroedinger equation. Interestingly, these solutions are all localized near the boundary. We further show that the number of bound states is finite and is in fact proportional to the perimeter or area of the removed \emph{disc} or \emph{ball}. We then argue that similar considerations should hold for static black hole backgrounds with the horizon treated as the boundary.

gr-qc↗

arXiv2010

Thermofield dynamics and twisted Poincaré symmetry on Moyal space-time

On Moyal space-time, one can implement twisted Poincaré symmetry with the resultant modification of symmetrization and anti-symmetrization postulates for bosons and fermions. We develop the thermofield approach of Umezawa and Takahashi on such a spacetime preserving the twisted Poincaré symmetry of the underlying quantum field theory(qft). Implications of this twisted Poincaré symmetry for qft's at finite temperature are pointed out.

hep-th↗

arXiv2009

Beyond fuzzy spheres

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level. Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra. This is seen in the measure constructed from these coherent states. We also find the star product for this non-commutative algebra as a first step in constructing field theories on such fuzzy spaces.

hep-th↗

arXiv2009

Deformed Oscillator Algebras and QFT in $κ$-Minkowski Spacetime

In this paper we study the deformed statistics and oscillator algebras of quantum fields defined in $κ$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of the Poincaré algebra to include the dilatation generators. Here we propose a novel notion of a fully covariant flip operator and show that to the first order in the deformation parameter it can be expressed completely in terms of the Poincaré generators alone. The $R$-matrices corresponding to the twisted and the covariant flip operators are compared up to first order in the deformation parameter and they are shown to be different. We also construct the deformed algebra of the creation and annihilation operators that arise in the mode expansion of a scalar field in $κ$-Minkowski spacetime. We obtain a large class of such new deformed algebras which, for certain choice of realizations, reduce to results known in the literature.

hep-th↗

arXiv2009

Spontaneous Symmetry Breaking in Twisted Noncommutative Quantum Theories

We analyse aspects of symmetry breaking for Moyal spacetimes within a quantisation scheme which preserves the twisted Poincaré symmetry. Towards this purpose, we develop the LSZ approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well.We also derive Goldstone's theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

hep-th↗

arXiv2008

Twisted Statistics in kappa-Minkowski Spacetime

We consider the issue of statistics for identical particles or fields in kappa-deformed spaces, where the system admits a symmetry group G. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription.

hep-th↗

arXiv2008

Spontaneous symmetry breakdown in fuzzy spheres

We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interactions present in these through geometrical considerations.

hep-th↗

arXiv2007

Finite temperature phase transition of a single scalar field on a fuzzy sphere

We study finite temperature phase transition of neutral scalar field on a fuzzy sphere using Monte Carlo simulations. We work with the zero mode in the temporal directions, while the effects of the higher modes are taken care by the temperature dependence of r. In the numerical calculations we use "pseudo-heatbath" method which reduces the auto-correlation considerably. Our results agree with the conventional calculations. We report some new results which show the presence of meta-stable states and also suggest that for suitable choice of parameters the symmetry breaking transition is of first order.

hep-th↗

arXiv2006

Statistics and UV-IR Mixing with Twisted Poincare Invariance

We elaborate on the role of quantum statistics in twisted Poincare invariant theories. It is shown that, in order to have twisted Poincare group as the symmetry of a quantum theory, statistics must be twisted. It is also confirmed that the removal of UV-IR mixing (in the absence of gauge fields) in such theories is a natural consequence.

hep-th↗

arXiv2006

Noncommutative Two Dimensional Gravities

We give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in the noncommutative theories as well. We argue that the existence of ``twisted'' diffeomorphisms, recently introduced in hep-th/0504183, is crucial for this conclusion.

hep-th↗

arXiv2006

Nonlocal regularisation of noncommutative field theories

We study noncommutative field theories, which are inherently nonlocal, using a Poincaré-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention onto the particular case when the noncommutativity parameter is inversely proportional to the square of the cut-off, via a dimensionless parameter $η$. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in $η$-dependent terms. The implications of this approach, which avoids the problems related to UV-IR mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.

hep-th↗

arXiv2005

Schwarz Type Topological Quantum Field Theories

Topological quantum field theories can be used to probe topological properties of low dimensional manifolds. A class of these theories known as Schwarz type theories, comprise of Chern-Simons theories and BF theories. In three dimensions both capture the properties of knots and links leading to invariants characterising them. These can also be used to construct three-manifold invariants. Three dimensional gravity is described by these field theories. BF theories exist also in higher dimensions. In four dimensions, these describe two-dimensional generalization of knots as well as Donaldson invariants.

hep-th↗

arXiv2005

Unitary Quantum Physics with Time-Space Noncommutativity

In this work quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. The Moyal plane is treated in detail. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schrodinger equation is studied. We prove in particular the following: suppose the Hamiltonian of a quantum mechanical particle on spacetime has no explicit time dependence, and the spatial coordinates commute in its noncommutative form (the only noncommutativity being between time and a space coordinate). Then the commutative and noncommutative versions of the Hamiltonian have identical spectra.

hep-th↗

arXiv2005

Time-Space Noncommutativity: Quantised Evolutions

In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and $\mathbb{R}\times S^{3}$. In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo $\frac{2π}θ$, where $θ$ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing $a$ and length $L=Na$, only momentum mod $\frac{2π}{L}$ is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined.

hep-th↗

arXiv2004

Non-commutative Duality: High Spin Fields and $CP^1$ Model with Hopf Term

We show that the non-commutative $CP^1$ model coupled with Hopf term in 3 dimensions is equivalent to an interacting spin-$s$ theory where the spin $s$ of the dual theory is related to the coefficient of the Hopf term. We use the Seiberg-Witten map in studying this non-commutative duality equivalence, keeping terms to order $θ$ and show that the spin of the dual theory do not get any $θ$ dependant corrections. The map between current correlators show that topological index of the solitons in the non-commutative $CP^1$ model is unaffected by $θ$ where as the Noether charge of the corresponding dual particle do get a $θ$ dependence. We also show that this dual theory smoothly goes to the limit $θ\to 0$ giving dual theory in the commutative plane.

hep-th↗

arXiv2003

O(3) Sigma model with Hopf term on Fuzzy Sphere

We formulate the $O(3) \s-$ model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be classified into different topological sectors by the magnetic quantum numbers. We obtain topological charge $Q$ and show that $-2j\le Q \le2j$. We also construct BPS solitons. Using the covariantly conserved current, we construct the Hopf term and show that its value is $Q^2$ as in the commutative case. We also point out the interesting relation of physical space to deformed SU(2) algebra.

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