arXiv subjects

Vincent G. J. Rodgers

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

11 recordsLinked to original sources

arXiv2024

Diffeomorphism Radiative Degrees of Freedom of Thomas-Whitehead Gravity

The geometric action of the semi-direct product of the Kac-Moody and Virasoro algebras contains the WZW action equipped with a background vector potential $A$ associated to a coadjoint element of the Kac-Moody algebra as well as the 2D gravitational Polyakov action and an accompanying background field, $\mathcal{D}$, called the diffeomorphism field. Just as the coadjoint element, $A$, is related to a gauge fixed Yang-Mills vector potential $A_a$, the diffeomorphism field, $\mathcal{D}$, is related to a component, $\mathcal{D}_{a b}$ of the projectively invariant connection called the Thomas Operator. The Yang-Mills action provides dynamics for the vector potential $A_a,$ while the Thomas-Whitehead (TW) gravitational action, provides dynamics to $\mathcal{D}_{ab}$. The TW action embeds the projectively invariant connection into a gravitational theory that contains general relativity. In this work, the diffeomorphism field $\mathcal{D}_{a b}$ is examined in Minkowski space where salient features of this field can be explored. In particular, we study the radiative degrees of freedom of this field while in a Minkowski space background. We show that it can be decomposed into irreducible representations, corresponding to tensor, vector, and scalar radiating solutions. Furthermore we examine geodesic deviation in the context of TW gravity about a Minkowski space background. We do this both at zeroth and first order in metric fluctuations $h_{ab}$. We discuss that response of a gravitational wave antennae to the geodesics deviations.

gr-qc↗

arXiv2022

From Virasoro Algebra to Cosmology

Earlier work of Balachandran and friends provided a map from algebras to field theories. These methods provide insight into quantum gauge theories and anomalies. In this note we take the reader from the coadjoint representation of the Virasoro algebra to four- (and higher-) dimensional gravitation and cosmology. The protagonist in this story is a component of the projective connection, the diffeomorphism field, which straddles between the one-dimensional world of initial data in string theories to cosmology in four dimensions. We review mathematical intuition that ties projective geometry to the Virasoro algebra, the Thomas\textendash Whitehead (TW) gravitational action that gives the diffeomorphism field dynamics and the building blocks for gauge projective Dirac action.

hep-th↗

arXiv2022

The Graded Extension of Thomas-Whitehead Gravity

Thomas-Whitehead (TW) gravity was recently introduced as a projective gauge theory of gravity over a d-dimensional manifold that embeds reparameterization invariance into the action functional for gravitation through the use of the Thomas-Whitehead connection. The projective invariance in this d-dimensional theory enjoys an intimate relationship with the Virasoro coadjoint elements found in string theory as one of the components of the connection, $\mathcal{D}_{ab}$, is directly related to the coadjoint elements of the Virasoro algebra. TW Gravity exploits projective Gauss-Bonnet terms in the action functional which allows the theory to collapse to Einstein's theory of General Relativity in the limit that $\mathcal{D}_{ab }$ vanishes. In this note we develop the graded extension of TW Gravity, Super TW Gravity, in the framework of a DeWitt supermanifold. We construct the Lagrangian for Super TW Gravity, give a detailed derivation of the classical field equations and discuss the graded extension of the projective connection as a prelude to a future understanding of TW-Supergravity (which has manifest supersymmetry) and its relationship to the Super-Virasoro algebra.

hep-th↗

arXiv2020

Dark Energy From Dynamical Projective Connections

We further develop the gravitational model, Thomas-Whitehead Gravity (TW Gravity), that arises when projective connections become dynamical fields. TW Gravity has its origins in geometric actions from string theory where the TW projective connection appears as a rank two tensor, $\mathcal{D}_{ab}$, on the spacetime manifold. Using a Gauss-Bonnet (GB) action built from the $(\mathrm{d}+1)$-dimensional TW connection, and applying the tensor decomposition $\mathcal{D}_{ab} = D_{ab} + 4Λ/(\mathrm{d}(\mathrm{d}-1)) g_{ab}$, we arrive at a gravitational model made up of a $\mathrm{d}$-dimensional Einstein-Hilbert + GB action sourced by $D_{ab}$ and with cosmological constant $Λ$. The $\mathrm{d}=4$ action is studied and we find that $Λ\propto 1/J_0$, with $J_0$ the coupling constant for $D_{ab}$. For $Λ$ equal to the current measured value, $J_0$ is on the order of the measured angular momentum of the observable Universe. We view this as $Λ$ controlling the scale of patches of the Universe that acquire angular momentum, with the net angular momentum of multiple patches vanishing, as required by the cosmological principle. We further find a universal axial scalar coupling to all fermions where the trace, $\mathcal{D} = \mathcal{D}_{ab}g^{ab}$ acts as the scalar. This suggests that $\mathcal{D}$ is also a dark matter portal for non-standard model fermions.

hep-th↗

arXiv2018

Dynamical Projective Curvature in Gravitation

By using a projective connection over the space of two-dimensional affine connections, we are able to show that the metric interaction of Polyakov 2D gravity with a coadjoint element arises naturally through the projective Ricci tensor. Through the curvature invariants of Thomas-Whitehead, we are able to define an action that could describe dynamics to the projective connection. We discuss implications of the projective connection in higher dimensions as related to gravitation.

hep-th↗

arXiv2016

Supergravity Solutions with $AdS_4$ from Non-Abelian T-Dualities

We present a large class of new backgrounds that are solutions of type II supergravity with a warped AdS${}_4$ factor, non-trivial axion-dilaton, B-field, and three- and five-form Ramond-Ramond fluxes. We obtain these solutions by applying non-Abelian T-dualities with respect to SU(2) or SU(2)/U(1) isometries to reductions to 10d IIA of 11d sugra solutions of the form AdS${}_4 \times Y^7$, with $Y^7 = S^7/\mathbb{Z}_k, S^7, M^{1,1,1}, Q^{1,1,1}$ and $N(1,1)$. The main class of reductions to IIA is along the Hopf fiber and leads to solutions of the form $AdS_4 \times K_6$, where $K_6 $ is Kähler Einstein with $K_6=\mathbb{CP}^3, S^2\times \mathbb{CP}^2, S^2\times S^2 \times S^2$; the first member of this class is dual to the ABJM field theory in the 't Hooft limit. We also consider other less symmetric but susy preserving reductions along circles that are not the Hopf fiber. In the case of $N(1,1)$ we find an additional breaking of isometries in the NAT-dual background. To initiate the study of some properties of the field theory dual, we explicitly compute the central charge holographically.

hep-th↗

arXiv2014

Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities

We present a large class of new backgrounds that are solutions of type IIB supergravity with a warped AdS${}_5$ factor, non-trivial axion-dilaton, $B$-field and three-form Ramond-Ramond flux but yet have no five-form flux. We obtain these solutions and many of their variations by judiciously applying non-Abelian and Abelian T-dualities, as well as coordinate shifts to AdS${}_5\times X_5$ IIB supergravity solutions with $X_5=S^5, T^{1,1}, Y^{p,q}$. We address a number of issues pertaining to charge quantization in the context of non-Abelian T-duality. We comment on some properties of the expected dual super conformal field theories by studying their CFT central charge holographically. We also use the structure of the supergravity Page charges, central charges and some probe branes to infer aspects of the dual super conformal field theories.

hep-th↗

arXiv2012

4D, N = 1 Supersymmetry Genomics (II)

We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, N = 1 systems, quark-like representations have been identified [1] in terms of cis-Adinkras and trans-Adinkras and it has been conjectured that arbitrary representations are composites of $n_c$-cis and $n_t$-trans representations. Analyzing the real scalar and complex linear superfield multiplets, these "chemical enantiomer" numbers are found to be $n_c$ = $n_t$ = 1 and $n_c$ = 1, $n_t$ = 2, respectively.

hep-th↗

arXiv2011

A Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.

hep-th↗

arXiv2009

Tensions and Luscher Terms for (2+1)-dimensional k-strings from Holographic Models

The leading term for the energy of a bound state of k-quarks and k-antiquarks is proportional to its separation L. These k-string configurations have a Luscher term associated with their quantum fluctuations which is typically a 1/L correction to the energy. We review the status of tensions and Luscher terms in the context of lattice gauge theory, Hamiltonian methods, and gauge/gravity correspondence. Furthermore we explore how different representations of the k-string manifest themselves in the gauge/gravity duality. We calculate the Luscher term for a strongly coupled SU(N) gauge theory in (2+1) dimensions using the gauge/gravity correspondence. Namely, we compute one-loop corrections to a probe D4-brane embedded in the Cvetic, Gibbons, Lu, and Pope supergravity background. We investigate quantum fluctuations of both the bosonic and the fermionic sectors.

hep-th↗

arXiv2008

Luscher Term for k-string Potential from Holographic One Loop Corrections

We perform a systematic analysis of k-strings in the framework of the gauge/gravity correspondence. We discuss the Klebanov-Strassler supergravity background which is known to be dual to a confining supersymmetric gauge theory with chiral symmetry breaking. We obtain the k-string tension in agreement with expectations of field theory. Our main new result is the study of one-loop corrections on the string theoretic side. We explicitly find the frequency spectrum for both the bosons and the fermions for quadratic fluctuations about the classical supergravity solution. Further we use the massless modes to compute 1/L contributions to the one loop corrections to the k-string energy. This corresponds to the Luscher term contribution to the k-string potential on the gauge theoretic side of the correspondence.

hep-th↗