arXiv subjects

Subhash Rajpoot

Publications and source records attributed to Subhash Rajpoot.

At least 73 records · Page 4Linked to original sources

arXiv2004

Octonions, G_2 Symmetry, Generalized Self-Duality and Supersymmetries in Dimensions D \le 8

We establish N=(1/8,1) supersymmetric Yang-Mills vector multiplet with generalized self-duality in Euclidian eight-dimensions with the original full SO(8) Lorentz covariance reduced to SO(7). The key ingredient is the usage of octonion structure constants made compatible with SO(7) covariance and chirality in 8D. By a simple dimensional reduction together with extra constraints, we derive N=1/8+7/8 supersymmetric self-dual vector multiplet in 7D with the full SO(7) Lorentz covariance reduced to G_2. We find that extra constraints needed on fields and supersymmetry parameter are not obtained from a simple dimensional reduction from 8D. We conjecture that other self-dual supersymmetric theories in lower dimensions D =6 and 4 with respective reduced global Lorentz covariances such as SU(3) \subset SO(6) and SU(2) \subset SO(4) can be obtained in a similar fashion.

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arXiv2004

Broken Scale Invariance in the Standard Model

We introduce Weyl's scale invariance as an additional local symmetry in the standard model of electroweak interactions. An inevitable consequence is the introduction of general relativity coupled to scalar fields a la Dirac and an additional vector particle we call the Weylon. We show that once Weyl's scale invariance is broken, the phenomenon (a) generates Newton's gravitational constant G_N and (b) triggers spontaneous symmetry breaking in the normal manner resulting in masses for the conventional fermions and bosons. The scale at which Weyl's scale symmetry breaks is of order Planck mass. If right-handed neutrinos are also introduced, their absence at present energy scales is attributed to their mass which is tied to the scale where scale invariance breaks.

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arXiv2004

Alephnull-Extended Supersymmetric Chern-Simons Theory for Arbitrary Gauge Groups

We present a model of supersymmetric non-Abelian Chern-Simons theories in three-dimensions with arbitrarily many supersymmetries, called alephnull-extended supersymmetry. The number of supersymmetry N equals the dimensionality of any non-Abelian gauge group G as N = dim G. Due to the supersymmetry parameter in the adjoint representation of a local gauge group G, supersymmetry has to be local. The minimal coupling constant is to be quantized, when the homotopy mapping is nontrivial: π_3(G) = Z. Our results indicate that there is still a lot of freedom to be explored for Chern-Simons type theories in three dimensions, possibly related to M-theory.

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arXiv2003

Supermembrane with Non-Abelilan Gauging and Chern-Simons Quantization

We present non-Abelian gaugings of supermembrane for general isometries for compactifications from eleven-dimensions, starting with Abelian case as a guide. We introduce a super Killing vector in eleven-dimensional superspace for a non-Abelian group G associated with the compact space B for a general compactification, and couple it to a non-Abelian gauge field on the world-volume. As a technical tool, we use teleparallel superspace with no manifest local Lorentz covariance. Interestingly, the coupling constant is quantized for the non-Abelian group G, due to its generally non-trivial mapping π_3(G).

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arXiv2003

Noncommutative Self-Dual Supersymmetric Yang-Mills Theory

We formulate noncommutative self-dual N=4 supersymmetric Yang-Mills theory in D=2+2 dimensions. As in the corresponding commutative case, this theory can serve as the possible master theory of all the noncommutative supersymmetric integrable models in lower dimensions. As a by-product, noncommutative self-dual N=2 supersymmetric Yang-Mills theory is obtained in D=2+2. We also perform a dimensional reduction of the N=2 theory further into N=(2,2) in D=1+1, as a basis for more general future applications. As a typical example, we show how noncommutative integrable matrix N=(1,0) supersymmetric KdV equations in D=1+1 arise from this theory, via the Yang-Mills gauge groups GL(n, R) or SL(2n, R).

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arXiv2003

Self-Dual Supergravity in Seven Dimensions with Reduced Holonomy G_2

We present self-dual N=2 supergravity in superspace for Euclidean seven dimensions with the reduced holonomy G_2 \subset SO(7), including all higher-order terms. As its foundation, we first establish N=2 supergravity without self-duality in Euclidean seven dimensions. We next show how the generalized self-duality in terms of octonion structure constants can be consistently imposed on the superspace constraints. We found two self-dual N=2 supergravity theories possible in 7D, depending on the representations of the two spinor charges of N=2. The first formulation has both of the two spinor charges in the {\bf 7} of G_2 with 24 + 24 on-shell degrees of freedom. The second formulation has both charges in the {\bf 1} of G_2 with 16 + 16 on-shell degrees of freedom.

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arXiv2003

Self-Dual N=(1,0) Supergravity in Eight Dimensions with Reduced Holonomy Spin(7)

We construct chiral N=(1,0) self-dual supergravity in Euclidean eight-dimensions with reduced holonomy Spin(7), including all the higher-order interactions in a closed form. We first establish the non-chiral N=(1,1) superspace supergravity in eight-dimensions with SO(8) holonomy without self-duality, as the foundation of the formulation. In order to make the whole computation simple, and the generalized self-duality compatible with supersymmetry, we adopt a particular set of superspace constraints similar to the one originally developed in ten-dimensional superspace. The intrinsic properties of octonionic structure constants make local supersymmetry, generalized self-duality condition, and reduced holonomy Spin(7) all consistent with each other.

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arXiv2003

Noncommutative Nonlinear Supersymmetry

We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4, 6 and 10.

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arXiv2002

Gauged N=2 Supergravity in Nine-Dimensions and Domain Wall Solutions

We present massive N=2 supergravity with SO(2)-gauging in nine-dimensions by direct construction. A full lagrangian and transformation rules are fixed, respectively up to quartic and quadratic fermion terms. Corresponding to the generalized Scherk-Schwarz dimensional reduction utilizing SL(2,R) symmetry, this theory allows three arbitrary mass parameters m_0, m_1and m_2 in addition to the minimal gauge coupling g, so that our system has the most general form compared with other results in the past. Unlike ordinary gauged maximal supergravity theories in other dimensions, the scalar potential is positive definite for arbitrary values of the mass parameters. As an application, we also analyze the stability and supersymmetry for 7-brane domain wall solutions for this gauged maximal supergravity, keeping the three mass parameters.

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arXiv2002

Topologican Gauging of N=16 Supergravity in Three-Dimensions

We present a topologically non-trivial generalization of gauged N=16 supergravity on the coset E_8 / SO(16) in three-dimensions. This formulation is based on a combination of BF-term and a Chern-Simons term for an SO(16) gauge field A_\m{}^{I J}. The fact that an additional vector field B_\m{}^{I J} is physical and propagating with couplings to σ-model fields makes our new gauging non-trivial and different from the conventional one. Even though the field strength of the A_\m{}^{I J}-field vanishes on-shell, the action is topologically non-trivial due to non-vanishing π_3-homotopy. We also present an additional modifications by an extra Chern-Simons term. As by-products, we give also an application to N=9 supergravity coupled to a σ-model on the coset F_4 / SO(9), and a new BF-Chern-Simons theory coupled to ^\forall N extended supergravity.

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arXiv2002

Generalized BF Theory in Superspace as Underlying Theory of 11D Supergravity

We construct a generalized BF theory in superspace that can embed eleven-dimensional supergravity theory. Our topological BF theory can accommodate all the necessary Bianchi identities for teleparallel superspace supergravity in eleven-dimensions, as the simplest but nontrivial solutions to superfield equations for our superspace action. This indicates that our theory may have solutions other than eleven-dimensional supergravity, accommodating generalized theories of eleven-dimensional supergravity. Therefore our topological theory can be a good candidate for the low energy limit of M-theory, as an underlying fundamental theory providing a `missing link' between eleven-dimensional supergravity and M-theory.

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arXiv2002

Axisymmetric Gravitational Solutions as Possible Classical Backgrounds around Closed String Mass Distributions

By studying singularities in stationary axisymmetric Kerr and Tomimatsu-Sato solutions with distortion parameter \d = 2, 3, ... in general relativity, we conclude that these singularities can be regarded as nothing other than closed string-like circular mass distributions. We use two different regularizations to identify \d-function type singularities in the energy-momentum tensor for these solutions, realizing a regulator independent result. This result gives supporting evidence that these axisymmetric exact solutions may well be the classical solutions around closed string-like mass distributions, just like Schwarzschild solution corresponding to a point mass distribution. In other words, these axisymmetric exact solutions may well provide the classical backgrounds around closed strings.

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arXiv2002

Supersymmetric E_{8(+8)} / SO(16) Sigma-Model Coupled to N=1 Supergravity in Three-Dimensions

A three-dimensional simple N=1 supergravity theory with a supersymmetric sigma-model on the coset E_{8(+8)} / SO(16) is constructed. Both bosons and fermions in the matter multiplets are in the spinorial 128-representation of SO(16) with the same chirality. Due to their common chirality, this model can not be obtained from the maximal N=16 supergravity. By introducing an independent vector multiplet, we can also gauge an arbitrary subgroup of SO(16) together with a Chern-Simons term. Similar N=1 supersymmetric sigma-models coupled to supergravity are also constructed for the cosets F_{4(-20)} / SO(9) and SO(8,n) / SO(8) X SO(n).

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arXiv2002

Teleparallel Complex Gravity as Foundation for Noncommutative Gravity

We present a teleparallel complex gravity as the foundation for the formulation of noncommutative gravity theory. The negative energy ghosts in the conventional formulation with U(1,3) local Lorentz connection no longer exists, since the local Lorentz invariance is broken down to U(1,3) global Lorentz symmetry. As desired, our teleparallel complex gravity theory also passes the key classical test of perihelion advance of Mercury. Based on this result, we present a lagrangian for the noncommutative teleparallel gravity theory.

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arXiv2001

Unimodular Supergravity

We present the locally supersymmetric formulation of unimodular gravity theory in D (1\le D \le 11) dimensions, namely supergravity theory with the metric tensor whose determinant is constrained to be unity. In such a formulation, the usual fine-tuning of cosmological constant is no longer needed, but its value is understood as an initial condition. Moreover, the zero-ness of the cosmological constant is concluded as the most probable configuration, based on the effective vacuum functional. We also show that the closure of supersymmetry gauge algebra is consistent with the unimodular condition on the metric.

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arXiv2001

Noncommutative Supersymmetric Yang-Mills Theory in Ten-Dimensions with Higher-Derivative Terms

We present an action for noncommutative supersymmetric Yang-Mills theory in ten-dimensions, and confirm its invariance under supersymmetry. We next add higher-order derivative terms to such a noncommutative supersymmetric action. These terms contain fields as high as the quartic order. This resulting action can be regarded as supersymmetric generalization of noncommutative non-Abelian Dirac-Born-Infeld action. Some ambiguities related to field redefinitions are also clarified.

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arXiv2001

Teleparallel Superspace in Eleven Dimensions Coupled to Supermembranes

We present a superspace formulation of N=1 eleven-dimensional supergravity with no manifest local Lorentz covariance, which we call teleparallel superspace. This formulation will be of great importance, when we deal with other supergravity theories in dimensions higher than eleven dimensions, or a possible formulation of noncommutative supergravity. As an illustrative example, we apply our teleparallel superspace formulation to the case of N=1 supergravity in twelve-dimensions. We also show the advantage of teleparallel superspace as backgrounds for supermembrane action.

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arXiv2001

A Note on Embedding of M-Theory Corrections into Eleven-Dimensional Superspace

By analyzing eleven-dimensional superspace fourth-rank superfield strength F-Bianchi identities, we show that M-theory corrections to eleven-dimensional supergravity can not be embedded into the mass dimension zero constraints, such as the (\g^{a b})_{\a\b} X_{a b}{}^c or i (\g^{a_1... a_5})_{\a\b} X_{a_1... a_5}{}^c -terms in the supertorsion constraint T_{\a\b}{}^c. The only possible modification of superspace constraint at dimension zero is found to be the scaling of F_{\a\b c d} like F_{\a\b c d} = (1/2) \big(\g_{c d}\big)_{\a\b} e^Φfor some real scalar superfield Φ, which alone is further shown not enough to embed general M-theory corrections. This conclusion is based on the dimension zero F-Bianchi identity under the two assumptions: (i) There are no negative dimensional constraints on the F-superfield strength: F_{\a\b\g\d} = F_{\a\b\g d} =0; (ii) The supertorsion T-Bianchi identities and F-Bianchi identities are not modified by Chern-Simons terms. Our result can serve as a powerful tool for future exploration of M-theory corrections embedded into eleven-dimensional superspace supergravity.

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