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Subhash Rajpoot

Publications and source records attributed to Subhash Rajpoot.

At least 55 records · Page 3Linked to original sources
arXiv2007

Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant

It has been recently shown that Nambu-Goto action can be re-expressed in terms of Cayley's hyperdeterminant with the manifest SL(2,R) X SL(2,R) X SL(2,R) symmetry. In the present paper, we show that the same feature is shared by Green-Schwarz sigma-model for N=2 superstring whose target space-time is D=2+2. When its zweibein field is eliminated from the action, it contains the Nambu-Goto action which is nothing but the square root of Cayley's hyperdeterminant of the pull-back in superspace \sqrt{\hyperdet(Π_{i \a\Dot\a})} manifestly invariant under SL(2,R) X SL(2,R) X SL(2,R). The target space-time D=2+2 can accommodate self-dual supersymmetric Yang-Mills theory. Our action has also fermionic kappa-symmetry, satisfying the criterion for its light-cone equivalence to Neveu-Schwarz-Ramond formulation for N=2 superstring.

hep-th↗
arXiv2007

Self-Dual Yang-Mills Multiplet in Three Dimensions Coupled to Supergravity

We couple a recently-established N=1 globally supersymmetric self-dual Yang-Mills multiplet in three dimensions to supergravity. This becomes possible due to our previous result on globally supersymmetric formulation based on a compensator multiplet. We further couple the self-dual vector to a supersymmetric sigma-model on the coset SO(8,n) / SO(8) X SO(n) via minimal couplings for an arbitrary gauged subgroup H_0 \subset SO(8) X SO(n). A corresponding superspace formulation is also presented.

hep-th↗
arXiv2007

N=4 Supersymmetric Yang-Mills Multiplet in Non-Adjoint Representations

We formulate a theory for N=4 supersymmetric Yang-Mills multiplet in a non-adjoint representation R of SO(N) as an important application of our recently-proposed model for N=1 supersymmetry. This system is obtained by dimensional reduction from an N=1 supersymmetric Yang-Mills multiplet in non-adjoint representation in ten dimensions. The consistency with supersymmetry requires that the non-adjoint representation R with the indices i, j, ... satisfy the three conditions η^{i j} = δ^{i j}, (T^I)^{i j} = - (T^I)^{j i} and (T^I)^{[ i j |} (T^I)^{| k ] l} = 0 for the metric η^{i j} and the generators T^I, which are the same as the N=1 case.

hep-th↗
arXiv2007

Supersymmetric Vector Multiplets in Non-Adjoint Representations of SO(N)

In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N) gauge group. Our basic algebra is [ T^I, T^J ] = f^{I J K} T^K, [ T^I, U^i ] = - (T^I)^{i j} U^j, [ U^i, U^j ] = - (T^I)^{i j} T^I, where T^I are the generators of SO(N), while U^i are the new 'generators' in certain non-adjoint real representation R of SO(N). We use here the word `generator' in the broader sense of the word. Such a representation can be any real representation of SO(N) with the positive definite metric, satisfying (T^I)^{i j} = - (T^I)^{j i} and (T^I)^{[ i j |} (T^I)^{| k ] l} \equiv 0. The first non-trivial examples are the spinorial 8_S and conjugate spinorial 8_C representations of SO(8) consistent with supersymmetry. We further couple the system to chiral multiplets, and show that a Higgs mechanism can give positive definite (mass)^2 to the new gauge fields for U^i. We show an analogous system working with N=1 supersymmetry in 10D, and thereby N=4 system in 4D interacting with extra multiplets in the representation R. We also perform superspace reformulation as an independent confirmation.

hep-th↗
arXiv2007

Gupta-Rajpoot Texture 2(4) Zero Mass Matrices

The so called ``Texture 2(4) zero mass matrices'' were first introduced in a Wayne State University preprint to accommodate the "yet to be discovered" heavy top quark. The preprint in its entirety is reproduced here after a brief commentary.

hep-ph↗
arXiv2007

Comment on Shadow and Non-Shadow Extensions of the Standard Model

The models in the two papers hep-ph/0608068 and hep-ph/0701254 by Chang et al. with the so-called shadow gauge and scalar fields are nothing but convenient tailored versions of our model in hep-th/0403039. The same remarks applies to the work in hep-th/0612165 by Meissner and Nicolai.

hep-th↗
arXiv2006

Nilpotent Spinor Symmetry with Interacting Spin 3/2 Field

Consistent interactions of spin 3/2 field that realize a nilpotent spinorial symmetry are presented. Based on our previous results on purely bosonic non-Abelian tensor with consistent interactions, we present a new system for interacting spin 3/2 field that realizes the nilpotent fermionic symmetry.

hep-th↗
arXiv2006

Self-Dual Non-Abelian Vector Multiplet in Three Dimensions

We present an N=1 supersymmetric non-Abelian compensator formulation for a vector multiplet in three-dimensions. Our total field content is the off-shell vector multiplet (A_μ^I, λ^I) with the off-shell scalar multiplet (ϕ^I, χ^I; F^I) both in the adjoint representation of an arbitrary non-Abelian gauge group. This system is reduced to a supersymmetric sigma-model on a group manifold, in the zero-coupling limit. Based on this result, we formulate a 'self-dual' non-Abelian vector multiplet in three-dimensions. By an appropriate identification of parameters, the mass of the self-dual vector multiplet is quantized. Additionally, we also show that the self-dual non-Abelian vector multiplet can be coupled to supersymmetric Dirac-Born-Infeld action. These results are further reformulated in superspace to get a clear overall picture.

hep-th↗
arXiv2006

(Curvature)^2-Terms for Supergravity in Three Dimension

We investigate the effect of (Curvature)^2-terms on N=1 and N=2 supergravity in three dimensions. We use the off-shell component fields (e_μ^m, ψ_μ, S) for N=1 and (e_μ^m, ψ_μ, ψ_μ^*, A_μ, B, B^*) for N=2 supergravity. The S, A_μand B are respectively a real scalar, a real vector and a complex scalar auxiliary fields. Both for N=1 and N=2, only two invariant actions for (Curvature)^2-terms exist, while only the actions with (Scalar Curvature)^2 are free of negative energy ghosts. Interestingly, the originally non-physical graviton and gravitino fields start propagating, together with the scalar field S for the N=1 case, or the complex scalar B and the longitudinal component \partial_μA^μfor N=2. These new propagating fields form two new physical massive supermultiplets of spins (1/2,0) with 2 x (1+1) degrees of freedom for the N=1 case, and two physical massive N=2 supermultiplets of spins (1/2,1/2,0,0) with 2 x (2+2) degrees of freedom for the N=2 case.

hep-th↗
arXiv2005

Interacting Vector-Spinor and Nilpotent Supersymmetry

We formulate an interacting theory of a vector-spinor field that gauges anticommuting spinor charges \{Q_α^I, Q_β^J \} = 0 in arbitrary space-time dimensions. The field content of the system is (ψ_μ^{αI}, χ^{αI J}, A_μ^I), where ψ_μ^{αI} is a vector-spinor in the adjoint representation of an arbitrary gauge group, and A_μ^I is its gauge field, while χ^{αI J} is an extra spinor with antisymmetric adjoint indices I J. Amazingly, the consistency of the vector-spinor field equation is maintained, despite its non-trivial interactions.

hep-th↗
arXiv2005

Non-Abelian Tensors with Consistent Interactions

We present a systematic method for constructing consistent interactions for a tensor field of an arbitrary rank in the adjoint representation of an arbitrary gauge group in any space-time dimensions. This method is inspired by the dimensional reduction of Scherk-Schwarz, modifying field strengths with certain Chern-Simons forms, together with modified tensorial gauge transformations. In order to define a consistent field strength of a r-rank tensor B_{μ_1...μ_r}^I in the adjoint representation, we need the multiplet (B_{μ_1...μ_r}^I, B_{μ_1...μ_{r-1}}^{I J}, ..., B_μ^{I_1...I_r}, B^{I_1... I_{r+1}}). The usual problem of consistency of the tensor field equations is circumvented in this formulation.

hep-th↗
arXiv2005

Aleph_null Hypergravity in Three-Dimensions

We construct hypergravity theory in three-dimensions with the gravitino ψ_{μm_1... m_n}{}^A with an arbitrary half-integral spin n+3/2, carrying also the index A for certain real representations of any gauge group G. The possible real representations are restricted by the condition that the matrix representation of all the generators are antisymmetric: (T^I)^{A B} = - (T^I)^{B A}. Since such a real representation can be arbitrarily large, this implies \aleph_0-hypergravity with infinitely many (\aleph_0) extended local hypersymmetries.

hep-th↗
arXiv2005

Dual Vector Multiplet Coupled to Dual N=1 Supergravity in 10D

We couple in superspace a `dual' vector multiplet (C_{m_1... m_7}, ł^α) to the dual version of N=1 supergravity (e_m{}^a, ψ_m{}^α, M_{m_1... m_6}, χ_\a,Φ) in ten-dimensions. Our new 7-form field C has its 8-form field strength H dual to the 2-form field strength F of the conventional vector multiplet. We have found that the H-Bianchi identity must have the form N\wedge F, where N is the 7-form field strength in dual supergravity. We also see why only the dual version of supergravity couples to the dual vector multiplet consistently. The potential anomaly for the dual vector multiplet can be cancelled for the particular gauge group U(1)^{496} by the Green-Schwarz mechanism. As a by-product, we also give the globally supersymmetric Abelian Dirac-Born-Infeld interactions for the dual vector multiplet for the first time.

hep-th↗
arXiv2004

Self-Dual Supersymmetric Dirac-Born-Infeld Action

We present a self-dual N=1 supersymmetric Dirac-Born-Infeld action in three dimensions. This action is based on the supersymmetric generalized self-duality in odd dimensions developed originally by Townsend, Pilch and van Nieuwenhuizen. Even though such a self-duality had been supposed to be very difficult to generalize to a supersymmetrically interacting system, we show that Dirac-Born-Infeld action is actually compatible with supersymmetry and self-duality in three-dimensions. The interactions can be further generalized to arbitrary (non)polynomial interactions. As a by-product, we also show that a third-rank field strength leads to a more natural formulation of self-duality in 3D. We also show an interesting role played by the third-rank field strength leading to a supersymmetry breaking, in addition to accommodating a Chern-Simons form.

hep-th↗
arXiv2004

Self-Dual Vector Multiplet in 3D with Gauged Scale Covariance

We present non-trivial interactions of N=1 self-dual massive vector multiplet in three-dimensions, with gauged scale covariance. Our multiplets are a vector multiplet (A_μ, λ) and a gauge multiplet (B_μ, χ), where the latter is used for the gauging of the scale covariance of the former. Due tothe absence of supergravity, this system has no lagrangian formulation, but has only a set of field equations. The gauge multiplet can also have Dirac-Born-Infeld type interactions, even in the presence of the massive self-dual vector multiplet. As a by-product, we also show that scale covariant couplings are possible for scalar multiplet. We also try a mechanism of spontaneous breaking of scale covariance by introducing a superpotential for scalar multiplets.

hep-th↗
arXiv2004

Hodge Duality and Cosmological Constant

We present a simple mechanism to eliminate cosmological constants both in supersymmetric and non-supersymmetric theories. This mechanism is based on the Hodge (Poincare) duality between a 0-form and D-form field strengths in D-dimensional space-time. The new key ingredient is the introduction of an extra Chern-Simons term into the D-form field strength H dual to the 0-form field strength. Our formulation can be also made consistent with supersymmetry. Typical applications to four-dimensional N=1 supergravity and to ten-dimensional type IIA supergravity are given. The success of our formulation for both supersymmetric and non-supersymmetric systems strongly indicates the validity of our mechanism even after supersymmetry breakings at the classical level. Our mechanism may well be applicable to quantized systems, at least for supersymmetric cases with fundamental D-brane actions available.

hep-th↗
arXiv2004

Supersymmetric Gauged Scale Covariance in Ten and Lower Dimensions

We present globally supersymmetric models of gauged scale covariance in ten, six, and four-dimensions. This is an application of a recent similar gauging in three-dimensions for a massive self-dual vector multiplet. In ten-dimensions, we couple a single vector multiplet to another vector multiplet, where the latter gauges the scale covariance of the former. Due to scale covariance, the system does not have a lagrangian formulation, but has only a set of field equations, like Type IIB supergravity in ten-dimensions. As by-products, we construct similar models in six-dimensions with N=(2,0) supersymmetry, and four-dimensions with N=1 supersymmetry. We finally get a similar model with N=4 supersymmetry in four-dimensions with consistent interactions that have never been known before. We expect a series of descendant theories in dimensions lower than ten by dimensional reductions. This result also indicates that similar mechanisms will work for other vector and scalar multiplets in space-time lower than ten-dimensions.

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