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M. B. Paranjape

Publications and source records attributed to M. B. Paranjape.

At least 55 records · Page 3Linked to original sources
arXiv2010

Phase transitions in a 3 dimensional lattice loop gas

We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise non-interacting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we find a phase transition as a function of their mass. We identify the order parameter as the average length of the loops at equilibrium. This order parameter exhibits a sharp increase as the mass is decreased through a critical value, the behaviour seems to be a cross-over transition. We believe that the model represents an effective description of the broken-symmetry sector of the 2+1 dimensional abelian Higgs model, in the extreme strong coupling limit. The massive gauge bosons and the neutral scalars are decoupled, and the relevant low-lying excitations correspond to vortices and anti-vortices. The functional integral can be approximated by a sum over simple, closed vortex loop configurations. We present a novel fashion to generate non-intersecting closed loops, starting from a tetrahedral tessellation of three space. The two phases that we find admit the following interpretation: the usual Higgs phase and a novel phase which is heralded by the appearance of effectively infinitely long loops. We compute the expectation value of the Wilson loop operator and that of the Polyakov loop operator. The Wilson loop exhibits perimeter law behaviour in both phases implying that the transition corresponds neither to the restoration of symmetry nor to confinement. The effective interaction between external charges is screened in both phases, however there is a dramatic increase in the polarization cloud in the novel phase as shown by the energy shift introduced by the Wilson loop.

hep-lat↗
arXiv2010

Phase transitions in a gas of anyons

We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however now in the presence of a topological term added to the action corresponding to the total linking number between the loops. We compute the linking number using certain notions from knot theory. Adding the topological term converts the particles into anyons. Using the correspondence that the model is an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. We find the following new results. The system continues to exhibit a phase transition as a function of the anyon mass as it becomes small \cite{mnp}, although the phases do not change the manifestation of the symmetry. The Chern-Simons term has no effect on the Wilson loop, but it does affect the {\rm '}t Hooft loop. For a given configuration it adds the linking number of the 't Hooft loop with all of the dynamical vortex loops to the action. We find that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, which is unexpected.

hep-lat↗
arXiv2010

Fate of the false monopoles: induced vacuum decay

We study a gauge theory model where there is an intermediate symmetry breaking to a meta- stable vacuum that breaks a simple gauge group to a U (1) factor. Such models admit the existence of meta-stable magnetic monopoles, which we dub false monopoles. We prove the existence of these monopoles in the thin wall approximation. We determine the instantons for the collective coordinate that corresponds to the radius of the monopole wall and we calculate the semi-classical tunneling rate for the decay of these monopoles. The monopole decay consequently triggers the decay of the false vacuum. As the monopole mass is increased, we find an enhanced rate of decay of the false vacuum relative to the celebrated homogeneous tunneling rate due to Coleman [1].

hep-th↗
arXiv2009

Gravitationally coupled magnetic monopole and conformal symmetry breaking

We consider a Georgi-Glashow model conformally coupled to gravity. The conformally invariant action includes a triplet of scalar fields and SO(3) non-Abelian gauge fields. However, the usual mass term $μ^2 ϕ^2$ is forbidden by the symmetry and this role is now played by the conformal coupling of the Ricci scalar to the scalar fields. Spontaneous symmetry breaking occurs via gravitation. The spherically symmetric solutions correspond to localized solitons (magnetic monopoles) in asymptotically anti-de-Sitter (AdS) space-time and the metric outside the core of the monopole is found to be Schwarzschild-AdS. Though conformal symmetry excludes the Einstein-Hilbert term in the original action, it emerges in the effective action after spontaneous symmetry breaking and dominates the low-energy/long-distance regime outside the core of the monopole.

gr-qc↗
arXiv2008

Suppression of quantum tunneling for all spins for easy-axis systems

The semi-classical limit of quantum spin systems corresponds to a dynamical Lagrangian which contains the usual kinetic energy, the couplings and interactions of the spins and an additional, first order kinematical term which corresponds to the Wess-Zumino-Novikov-Witten (WZNW) term for the spin degree of freedom \cite{og}. It was shown that in the case of the kinetic dynamics determined only by the WZNW term, half odd integer spin systems show a lack of tunneling phenomena whereas integer spin systems are subject to it \cite{l} in the case of potentials with easy-plane easy-axis symmetry. Here we prove, for the theory with a normal quadratic kinetic term of arbitrary strength or the first order theory with azimuthal symmetry (which is equivalently the so-called easy-axis situation), that the tunneling is in fact suppressed for all non-zero values of spin. This model exemplifies the concept that in the presence of complex Euclidean action, it is necessary to use the ensuing complex critical points in order to define the quantum (perturbation) theory \cite{ampr}. In the present example, if we do not do so, exactly the opposite, erroneous conclusion, that the tunneling is unsuppressed for all spins, is reached.

hep-th↗
arXiv2008

Spontaneous breaking of conformal invariance, solitons and gravitational waves in theories of conformally invariant gravitation

We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we require a mechanism for the spontaneous breaking of conformal invariance. In this paper we study the possibility that conformal invariance is spontaneously broken due to interactions with conformally coupled matter fields. The vacuum of the theory admits conformally non-invariant solutions corresponding to maximally symmetric space-times and variants thereof. These are either de Sitter space-time or anti-de Sitter space-time in the full four space-time dimensions or in a lower dimensional sub-space. We consider in particular normalizable, linearized gravitational perturbations around the anti-de Sitter background. Exploiting the conformal flatness of this space-time, we show to second order, that these gravitational fluctuations, that are taken to be fourier decomposable, carry zero energy-momentum. This squares well with the theorem that asymptotically flat space-times conformal gravity contain zero energy and momentum \cite{bhs}. We also show the possibility of domain wall solitons interpolating between the ground states of spontaneously broken conformal symmetry that we have found. These solitons necessarily require the vanishing of the scalar field, repudiating the recent suggestion \cite{f} that the conformal symmetry could be quarantined to a sterile sector of the theory by choosing an appropriate field redefinition.

hep-th↗
arXiv2008

Path integration and perturbation theory with complex Euclidean actions

The Euclidean path integral quite often involves an action that is not completely real {\it i.e.} a complex action. This occurs when the Minkowski action contains $t$-odd CP-violating terms. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, what is done is that only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory. In this article we present a simple 0+1-dimensional example, of $N$ scalar fields interacting with a U(1) gauge field, in the presence of a Chern-Simons term, where alternatively, the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show explicitly that the standard method does not give a correct perturbative expansion.

hep-th↗
arXiv2007

Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory

We study Maxwell-Chern-Simons theory in 2 noncommutative spatial dimensions and 1 temporal dimension. We consider a finite matrix model obtained by adding a linear boundary field which takes into account boundary fluctuations. The pure Chern-Simons has been previously shown to be equivalent to the Laughlin description of the quantum Hall effect. With the addition of the Maxwell term, we find that there exists a rich spectrum of excitations including solitons with nontrivial "magnetic flux" and quasi-holes with nontrivial "charges", which we describe in this article. The magnetic flux corresponds to vorticity in the fluid fluctuations while the charges correspond to sources of fluid fluctuations. We find that the quasi-hole solutions exhibit a gap in the spectrum of allowed charge.

hep-th↗
arXiv2007

Field theoretic description of the abelian and non-abelian Josephson effect

We formulate the Josephson effect in a field theoretic language which affords a straightforward generalization to the non-abelian case. Our formalism interprets Josephson tunneling as the excitation of pseudo-Goldstone bosons. We demonstrate the formalism through the consideration of a single junction separating two regions with a purely non-abelian order parameter and a sandwich of three regions where the central region is in a distinct phase. Applications to various non-abelian symmetry breaking systems in particle and condensed matter physics are given.

hep-ph↗
arXiv2006

Problems With Complex Actions

We consider Euclidean functional integrals involving actions which are not exclusively real. This situation arises, for example, when there are $t$-odd terms in the the Minkowski action. Writing the action in terms of only real fields (which is always possible), such terms appear as explicitly imaginary terms in the Euclidean action. The usual quanization procedure which involves finding the critical points of the action and then quantizing the spectrum of fluctuations about these critical points fails. In the case of complex actions, there do not exist, in general, any critical points of the action on the space of real fields, the critical points are in general complex. The proper definition of the function integral then requires the analytic continuation of the functional integration into the space of complex fields so as to pass through the complex critical points according to the method of steepest descent. We show a simple example where this procedure can be carried out explicitly. The procedure of finding the critical points of the real part of the action and quantizing the corresponding fluctuations, treating the (exponential of the) complex part of the action as a bounded integrable function is shown to fail in our explicit example, at least perturbatively.

hep-th↗
arXiv2006

Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, providing a mechanism for supplying a scale in the theory. The vacuum solution corresponds to anti-de-Sitter space-time, while localized soliton solutions correspond to magnetic monopoles in asymptotically anti-de-Sitter space-time. The resulting effective action gives rise to Einstein gravity and the residual U(1) gauge theory. This mechanism strengthens the reasons for considering conformally invariant matter-gravity theory, which has shown promising indications concerning the problem of missing matter in galactic rotation curves.

hep-th↗
arXiv2005

Solitons in finite droplets of noncommutative Maxwell-Chern-Simons theory

We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their flux and their energies. The model we consider is directly related to the model proposed by Polychronakos\cite{Poly} and studied by Hellerman and Van Raamsdonk\cite{HvR} where it was shown that it is equivalent to the quantum Hall effect.

hep-th↗
arXiv2003

On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory

We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive ``plane wave'' solutions with polarization dependent on the magnitude of the wave-vector. The mass of each branch is fixed by the quantization condition imposed on the coefficient of the noncommutative Chern-Simons term. For the radially symmetric ansatz a vortex-like solution is found and investigated. We derive a nonlinear difference equation describing these solutions and we find their asymptotic form. These excitations should be relevant in describing the Quantum Hall transitions between plateaus and the end transition to the Hall Insulator.

hep-th↗
arXiv2001

From Q-walls to Q-balls

We study $Q$-ball type solitons in arbitrary spatial dimensions in the setting recently described by Kusenko, where the scalar field potential has a flat direction which rises much slower than $ϕ^2$. We find that the general formula for energy as a function of the charge is, $E_d\sim Q_d^{(d/d+1)}$ in spatial dimension $d$. We show that the Hamiltonian governing the stability analysis of certain $Q$-wall configurations, which are one dimensional $Q$-ball solutions extended to planar, wall-like configurations in three dimensions, can be related to supersymmetric quantum mechanics. $Q$-wall and $Q$-string (the corresponding extensions of 2 dimensional $Q$-balls in 3 spatial dimensions) configurations are seen to be unstable, and will tend to bead and form planar or linear arrays of 3 dimensional $Q$-balls. The lifetime of these wall-like and string-like configurations is, however, arbitrarily large and hence they could be of relevance to cosmological density fluctuations and structure formation in the early Universe.

hep-th↗
arXiv2001

Solitons in 2+1 Dimensional Non-Commutative Maxwell Chern-Simons Higgs Theories

We find soliton solutions in the 2+1 dimensional non-commutative Maxwell Chern-Simons Higgs theories. In the limit of the Chern-Simons coefficient going to zero, these solutions go over to the previously found solutions in the non-commutative Maxwell Higgs theories. The new solutions may have relevance in the theory of the fractional quantum Hall effect and possibly in string vacua corresponding to open strings terminating on D2 branes in the presence of D0 branes.

hep-th↗
arXiv2000

Topological symmetry breaking and the confinement of anyons

We study topological symmetry breaking via the behaviour of Wilson and 't Hooft loop operators for the 2+1 dimenesional Abelian-Higgs model with Chern-Simons term. The topological linking of instantons, which are closed vortex loop configurations, give rise to a long-range, logarithmic, confining potential between electric charges and magnetic flux tubes even though all perturbative forces are short range. Gauss' law forces the concomitance of charge and magnetic flux, hence the confinement is actually of anyons.

hep-th↗
arXiv2000

Gauge choice and geodetic deflection in conformal gravity

Conformal gravity has been proposed as an alternative theory of gravity which can account for flat galactic rotation curves without recourse to copious quantities of dark matter. However it was shown that for the usual choice of the metric, the result is catastrophic for null or highly relativistic geodesics, the effect is exactly the opposite yielding an effective repulsion and less deflection in this case. It is the point of this paper, that any result for massive geodesics depends on the choice of conformal gauge, in contradistinction to the case of null geodesics. We show how it is possible to choose the gauge so that the theory is attractive for all geodesics.

astro-ph↗