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V. G. J. Rodgers

Publications and source records attributed to V. G. J. Rodgers.

At least 19 recordsLinked to original sources
arXiv2009

4D, N = 1 Supersymmetry Genomics (I)

Presented in this paper the nature of the supersymmetrical representation theory behind 4D, N = 1 theories, as described by component fields, is investigated using the tools of Adinkras and Garden Algebras. A survey of familiar matter multiplets using these techniques reveals they are described by two fundamental valise Adinkras that are given the names of the cis-Valise (c-V) and the trans-Valise (t-V). A conjecture is made that all off-shell 4D, N = 1 component descriptions of supermultiplets are associated with two integers - the numbers of c-V and t-V Adinkras that occur in the representation.

hep-th↗
arXiv2009

A Geometric Action for the Courant Bracket

An important operation in generalized complex geometry is the Courant bracket which extends the Lie bracket that acts only on vectors to a pair given by a vector and a p-form. We explore the possibility of promoting the elements of the Courant bracket to physical fields by constructing a geometric action based on the Kirillov-Kostant symplectic form. For the $p=0$ forms, the action generalizes Polyakov's two-dimensional quantum gravity when viewed as the geometric action for the Virasoro algebra. We show that the geometric action arising from the centrally extended Courant bracket for the vector and zero form pair is similar to the geometric action obtained from the semi-direct product of the Virasoro algebra with a U(1) affine Kac-Moody algebra. For arbitrary $p$ restricted to a Dirac structure, we derived the geometric action and exhibit generalizations for almost complex structures built on the Kirillov-Kostant symplectic form. In the case of p+1 dimensional submanifolds, we also discuss a generalization of a Kahler structure on the orbits.

hep-th↗
arXiv2006

General Coordinate Transformations as the Origins of Dark Energy

In this note we demonstrate that the algebra associated with coordinate transformations might contain the origins of a scalar field that can behave as an inflaton and/or a source for dark energy. We will call this particular scalar field the diffeomorphism scalar field. In one dimension, the algebra of coordinate transformations is the Virasoro algebra while the algebra of gauge transformations is the Kac-Moody algebra. An interesting representation of these algebras corresponds to certain field theories that have meaning in any dimension. In particular the so called Kac-Moody sector corresponds to Yang-Mills theories and the Virasoro sector corresponds to the diffeomorphism field theory that contains the scalar field and a rank-two symmetric, traceless tensor. We will focus on the contributions of the diffeomorphism scalar field to cosmology. We show that this scalar field can, qualitatively, act as a phantom dark energy, an inflaton, a dark matter source, and the cosmological constant Lambda.

hep-th↗
arXiv2003

Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras

We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N-extended supersymmetric GR Virasoro algebra.

hep-th↗
arXiv2002

Superspace Geometrical Realization of the N-Extended Super Virasoro Algebra and its Dual

We derive properties of N-extended GR super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification with the spectrum of fields in supergravity theories and superstring/M-theory constructed from NSR N-extended supersymmetric ${\cal {GR}}$ Virasoro algebras.

hep-th↗
arXiv2002

Chiral Supergravitons Interacting with a 0-Brane N-Extended NSR Super-Virasoro Group

We continue the development of the actions, S_{AFF}, by examining the cases where there are N fermionic degrees of freedom associated with a 0-brane. These actions correspond to the interaction of the N-extended super Virasoro algebra with the supergraviton and the associated SO(N) gauge field that accompanies the supermultiplet. The superfield formalism is used throughout so that supersymmetry is explicit.

hep-th↗
arXiv2001

Super Gravitons Interacting with the Super Virasoro Group

We describe actions that correspond to the interaction of the Super Virasoro algebra with supergravitons. These new field theories introduce a superfield that corresponds to dual elements of the super Virasoro algebra. We are also able to extend the definition of these field theories to higher dimensions. We explicitly exhibit the 2, 3 and 4 dimensional cases. Remarkably, the fundamental prepotentials describing these dual elements of the super Virasoro algebra, in each model, agrees with the known prepotentials of the corresponding supergravity theory. These theories might be important in the quantization of the super Virasoro group, supergravity and in AdS and super AdS gravity.

hep-th↗
arXiv2000

Irreducible Decomposition of Products of 10D Chiral Sigma Matrices

We review the enveloping algebra of the 10 dimensional chiral sigma matrices. To facilitate the computation of the product of several chiral sigma matrices we have developed a symbolic program. Using this program one can reduce the multiplication of the sigma matrices down to linear combinations of irreducilbe elements. We are able to quickly derive several identities that are not restricted to traces. A copy of the program written in the Mathematica language is provided for the community.

hep-th↗
arXiv2000

Interactions of a String Inspired Graviton Field

We continue to explore the possibility that the graviton in two dimensions is related to a quadratic differential that appears in the anomalous contribution of the gravitational effective action for chiral fermions. A higher dimensional analogue of this field might exist as well. We improve the defining action for this diffeomorphism tensor field and establish a principle for how it interacts with other fields and with point particles in any dimension. All interactions are related to the action of the diffeomorphism group. We discuss possible interpretations of this field.

hep-th↗
arXiv2000

The Image of Self Intersecting QCD Strings in Four Dimensions

We numerically examine the self-dual solutions of self-intersecting strings immersed in four dimensions. We find that open torus knots have topologies that can support monopole/anti-monopole as well as q-qbar production and annihilation. We give an estimate of the string tension from quark production rates, show that the intersection number for torus-knots is 4(p-q), and discuss a chiral symmetry breaking mechanism due to self-intersections. We supply a MAPLE program that can annimate the torus-knot solutions. These annimations can be found at http://www-hep.physics.uiowa.edu/~bacus/research.html under the ``Animation Control Panel''.

hep-th↗
arXiv1997

Yang-Mills, Gravity, and String Symmetries

In this work we use constructs from the dual space of the semi-direct product of the Virasoro algebra and the affine Lie algebra of a circle to write a theory of gravitation which is a natural analogue of Yang-Mills theory. The theory provides a relation between quadratic differentials in 1+1 dimensions and rank two symmetric tensors in higher dimensions as well as a covariant local Lagrangian for two dimensional gravity. The isotropy equations of coadjoint orbits are interpreted as Gauss law constraints for a field theory in two dimensions, which enables us to extend to higher dimensions. The theory has a Newtonian limit in any space-time dimension. Our approach introduces a novel relationship between string theories and 2D field theories that might be useful in defining dual theories. We briefly discuss how this gravitational field couples to fermions.

hep-th↗
arXiv1997

Type -B/ -O Bosonic String Sigma-Models

We provide world sheet non-supersymmetrical actions that describe the coupling of a bosonic string to the tachyon and massless states of both the type-B and type-O theories. The type-B theory is derived as a truncation and chiral doubling of the Ramond-Ramond sector in our previous model that connected the (1,0) heterotic string to a 10 D type IIB supergravity background. The type-O theory then follows from a ``fermionization'' of the type-B theory.

hep-th↗
arXiv1996

Yang-Mills, Gravity, and 2D String Symmetries

It is well known that by using the infinite dimensional symmetries that issue from string theories, one can build 2D geometric field theories. These 2D field theories can be identified with gravitational and gauge anomalies that arise in the presence of background gauge and gravitational anomalies. In this work we consider the background fields as residuum from reducing higher dimensional field theories to two dimensions. This implies a new relationship between string theory and field theories. We identify the isotropy equations of the distinct orbits as the Gauß's law constraints of a Yang-Mills theory coupled to a gravitational theory that has been evaluated on a two-dimensional manifold. We show explicitly how one may recover the higher dimensional theories and extract this new theory of gravity and its coupling to Yang-Mills theory. This gravitational theory is able to couple to Yang-Mills via a torsion-like term and yet maintain gauge invariance. Also this new theory of gravity suggest a natural distinction between cosmology and local gravitation. We comment on the analogue of Chern-Simons theory for diffeomorphism, the vacuum structure of gravity, and also the possibility of extracting explicit realizations of distinct differentiable structures in four dimensions.

hep-th↗
arXiv1995

Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.

hep-lat↗
arXiv1994

A 2D Inspired 4D Theory of Gravity

Coadjoint orbits of the Virasoro and Kac-Moody algebras provide geometric actions for matter coupled to gravity and gauge fields in two dimensions. However, the Gauss' law constraints that arise from these actions are not necessarily endemic to two-dimensional topologies. Indeed the constraints associated with Yang-Mills naturally arise from the coadjoint orbit construction of the WZW model. One may in fact use a Yang-Mills theory to provide dynamics to the otherwise fixed coadjoint vectors that define the orbits. In this letter we would like to exhibit an analogue of the Yang-Mills classical action for the diffeomorphism sector. With this analogue one may postulate a 4D theory of gravitation that is related to an underlying two dimensional theory. Instead of quadratic differentials, a (1,3) pseudo tensor becomes the dynamical variable. We briefly discuss how this tensor may be classically coupled to matter.

hep-th↗
arXiv1994

A Study of Fermions Coupled to Gauge and Gravitational Fields on a Cylinder

Fermions on a cylinder coupled to gravity and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. The gauge coupling constant is shown to be constrained and the effect of gravity on the masses is discussed. Furthermore, we introduce a new gravitational theory which couples to the fermions by promoting the coadjoint vector of the diffeomorphism sector to a dynamical variable. This system, together with the gauge sector is shown to be equivalent to a one dimensional system.

hep-th↗
arXiv1994

A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion

We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($σ=\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using recursive methods which exploit the symmetries of the model. Lattices with up to $2^18$ sites have been used. Surprisingly, the numerical data can be fitted very well with a simple power law of the form $(1- β/β_c )^{- γ} $for the {\it whole} temperature range. The numerical values for $γ$ agree within a few percent with the values calculated with a high-temperature expansion but show significant discrepancies with the epsilon-expansion. We would appreciate comments about these results.

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