arXiv subjects
Publications and source records attributed to Ashok Das.
The breaking of supersymmetry due to singular potentials in supersymmetric quantum mechanics is critically analyzed. It is shown that, when properly regularized, these potentials respect supersymmetry, even when the regularization parameter is removed.
In this paper, we extend our earlier one loop analysis to two loops and give a simple diagrammatic description for the retarded Greens functions at finite temperature, in terms of forward scattering amplitudes of on-shell thermal particles. We present a simple discussion, which can be easily generalized to any field theory, of the temperature dependent parts of the retarded two and three point functions in scalar field theory and QED. As an application of our result at two loops, we show how the infrared singularities in the thermal part of the retarded photon self-energy, cancel in QED_2 in the limit of vanishing electron mass.
In this brief report, we analyze a generalized theory of massless scalar QED_2 and show that, unlike the conventional scalar QED_2, it is free from infrared divergence problems. The model is exactly soluble and may describe, in an 1+1 dimensional space-time, noninteracting spin-one tachyons.
We compute the effective actions for the 0+1 dimensional scalar field interacting with an Abelian gauge background, as well as for its supersymmetric generalization at finite temperature.
In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time formalism. Furthermore, we give a simple calculational method for evaluating the temperature dependent parts of the retarded vertex functions, to one loop, by identifying them with the forward scattering amplitudes of on-shell thermal particles. As an application of the method, we calculate and show that the temperature dependent parts of all the retarded functions vanish at one loop order for 1+1 dimensional massless QED. We further point out that, in this model, in fact, the temperature dependent parts of all the retarded vertex functions vanish to all orders in perturbation theory.
In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of 1+1 dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum corrections). The covariant structure thus obtained may prove useful in studying 2+1 dimensional models in arbitrary backgrounds. We also comment briefly on the solubility of various 1+1 dimensional models at finite temperature.
We show how Schwinger's proper time method can be used to evaluate directly the determinant of first order operators associated with fermionic theories. Several examples are worked out in detail.
We study the 0+1 dimensional Chern-Simons theory at finite temperature within the framework of derivative expansion. We obtain various interesting relations, solve the theory within this framework and argue that the derivative expansion is not a suitable formalism for a study of the question of large gauge invariance.
We derive the Dirac brackets for the O(N) nonlinear sigma model in the lightfront description with and without the constraint. We bring out various subtleties that arise including the fact that anti-periodic boundary condition seems to be preferred.
We study the Born-Infeld equation from a Lagrangian point of view emphasizing the duality symmetry present in such systems. We obtain the Hamiltonian formulation directly from the Lagrangian. We also show that this system admits a dispersionless nonstandard Lax representation which directly leads to all the conserved charges (including the ones not previously obtained). We also present the generating function for these charges and point out various other properties of this system.
We examine finite temperature perturbation theory for Chern-Simons theories, in the context of an analogue 0+1-dimensional model. In particular, we show how nonextensive terms arise in the perturbative finite temperature effective action, using both the real-time and imaginary-time formalisms. We illustrate how large gauge invariance is restored at all orders, despite being broken at any given order in perturbation theory. We discuss which aspects generalize to a perturbative analysis of finite temperature Chern-Simons terms in higher dimensions.
We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.
We study, systematically, the properties of the supersymmetric AKNS (sAKNS) hierarchy. In particular, we discuss the Lax representation in terms of a bosonic Lax operator and some special features of the equations and construct the bosonic local charges as well as the fermionic nonlocal charges associated with the system starting from the Lax operator. We obtain the Hamiltonian structures of the system and check the Jacobi identity through the method of prolongation. We also show that this hierarchy of equations can equivalently be described in terms of a fermionic Lax operator. We obtain the zero curvature formulation as well as the conserved charges of the system starting from this fermionic Lax operator which suggests a connection between the two. Finally, starting from the fermionic description of the system, we construct the soliton solutions for this system of equations through Darboux-Backlund transformations and describe some open problems.
It is well-known that the conjectured SL(2, Z) invariance of type IIB string theory in ten dimensions also persists in lower dimensions when the theory is compactified on tori. By making use of this recent observation, we construct an infinite family of magnetically charged black hole solutions of type II superstring theory in four space-time dimensions. These solutions are characterized by two relatively prime integers corresponding to the magnetic charges associated with the two gauge fields (from NS-NS and R-R sectors) of the theory and form an SL(2, Z) multiplet. In the extremal limit these solutions are stable as they are prevented from decaying into black holes of lower masses by a `mass gap' equation.
The electric dipole moment of the muon ($d_μ$) is evaluated in a two Higgs doublet model with a softly broken discrete symmetry. For $\tanβ\equiv |v_2|/|v_1| \sim 1$, contributions from two loop diagrams involving the $t$ quark and the $W$ boson dominate; while for $\tanβ\gsim 10$, contributions from two loop diagrams involving the $b$ quark and the $τ$ lepton are dominant. For $8 \gsim \tanβ\gsim 4$, significant cancellation occurs among the contributions from two loop diagrams and the one loop contribution dominates for $\tanβ\sim 7$. For $\tanβ\gsim 15$, the calculated $d_μ$ can be close to the reach of a recently proposed experiment at the Brookhaven National Laboratory.
We have constructed the N=1/2 supersymmetric general Abelian model with asymmetric chiral couplings. This leads to a N=1/2 supersymmetrization of the Schwinger model. We show that the supersymmetric general model is plagued with problems of infrared divergence. Only the supersymmetric chiral Schwinger model is free from such problems and is dynamically equivalent to the chiral Schwinger model because of the peculiar structure of the N=1/2 multiplets.
The electric dipole moment of the muon ($d_μ$) is evaluated in a two Higgs doublet model with a softly broken discrete symmetry. The leading contributions from both one loop and two loop diagrams are considered. For $\tanβ\equiv |v_2|/|v_1|$ close to one, contributions from two loop diagrams involving the $t$ quark and the $W$ boson dominate; while for $\tanβ\agt 10$, contributions from two loop diagrams involving the $b$ quark and the $τ$ lepton are dominant. In these two regions, $d_μ\approx (m_μ/m_e) d_e$. For $8 \agt \tanβ\agt 4$, significant cancellation occurs among the contributions from two loop diagrams and the one loop contribution dominates for $\tanβ\sim 7$. For $\tanβ\agt 15$, the calculated $d_μ$ can be close to the reach of a recently proposed experiment at the Brookhaven National Laboratory.
A new mechanism for symmetry breaking is proposed which naturally avoids the constraints following from the usual theorems of symmetry breaking. In the context of super-symmetry, for example, the breaking may be consistent with a vanishing vacuum energy. A 2+1 dimensional super-symmetric gauge field theory is explicitly shown to break super-symmetry through this mechanism while maintaining a zero vacuum energy. This mechanism may provide a solution to two long standing problems, namely, dynamical super-symmetry breaking and the cosmological constant problem.