arXiv subjects

David S. Berman

Publications and source records attributed to David S. Berman.

At least 37 records · Page 2Linked to original sources

arXiv2020

Weyl doubling

We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordstrom metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

hep-th↗

arXiv2020

S-duality and the Double Copy

The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical solutions in gauge theories such as the monopole and instanton. In this paper we will investigate how duality symmetries in the gauge theory double copy to gravity and relate these to solution generating transformations and the action of $Sl(2,R)$ in general relativity.

hep-th↗

arXiv2020

Reductions of Exceptional Field Theories

Double Field Theory (DFT) and Exceptional Field Theory (EFT), collectively called ExFTs, have proven to be a remarkably powerful new framework for string and M-theory. Exceptional field theories were constructed on a case by case basis as often each EFT has its own idiosyncrasies. Intuitively though, an $E_{n-1(n-1)}$ EFT must be contained in an $E_{n(n)}$ ExFT. In this paper we propose a generalised Kaluza-Klein ansatz to relate different ExFTs. We then discuss in more detail the different aspects of the relationship between various ExFTs including the coordinates, section condition and (pseudo)-Lagrangian densities. For the $E_{8(8)}$ EFT we describe a generalisation of the Mukhi-Papageorgakis mechanism to relate the d = 3 topological term in the $E_{8(8)}$ EFT to a Yang-Mills action in the $E_{7(7)}$ EFT.

hep-th↗

arXiv2019

Non-Riemannian geometry of M-theory

We construct a background for M-theory that is moduli free. This background is then shown to be related to a topological phase of the $\mathrm{E}_{8(8)}$ exceptional field theory (ExFT). The key ingredient in the construction is the embedding of non-Riemannian geometry in ExFT. This allows one to describe non-relativistic geometries, such as Newton-Cartan or Gomis-Ooguri-type limits, using the ExFT framework originally developed to describe maximal supergravity. This generalises previous work by Morand and Park in the context of double field theory.

hep-th↗

arXiv2019

Exotic Branes in M-Theory

We revisit curious objects in string and M-theory called exotic brane---objects that are highly non-perturbative, possessing a tension that scales less than $g_s^{-2}$ and are generically of low-codimension. They are non-geometric in the sense that they are only well-defined locally as supergravity solutions and require duality transformations to patch correctly, in addition to the usual diffeomorphisms and gauge transformations. We argue that Double Field Theory (DFT) and Exceptional Field Theory (EFT) are the prime setting in which to examine such objects. To emphasise this, we construct an explicit solution in $E_{7(7)} \times \mathbb{R}^+$ EFT that unifies many of the codimension-2 exotic branes into a single well-behaved solution on an extended spacetime. We further argue that there are in fact an infinite number of exotic branes in string- and M-theory, many of which fall into a more general class of exotic branes that do not afford even a local description in terms of conventional supergravity.

hep-th↗

arXiv2019

A Kaluza-Klein Approach to Double and Exceptional Field Theory

We examine the challenge of viewing all the fields in supergravity as arising from a Kaluza-Klein like dimensional reduction of some higher-dimensional theory. This gives rise to what is known as exceptional field theory or double field theory. A particular emphasis is placed on following the Kaluza-Klein intuition leading to the identification of charged states and a reinterpretation of the central charges. We further give a description of the novel extended geometry as a generalised phase space and the relationship to string and M-theory theory and the notion of quantization

hep-th↗

arXiv2018

The self-dual classical double copy, and the Eguchi-Hanson instanton

The double copy is a map from non-abelian gauge theories to gravity, that has been demonstrated both for scattering amplitudes and exact classical solutions. In this study, we reconsider the double copy for exact solutions that are self-dual in either the gauge or gravity theory. In this case, one may formulate a general double copy in terms of a certain differential operator, which generates the gauge and gravity solutions from a harmonic function residing in a biadjoint scalar theory. As an illustration, we examine the single copy of the well-known Eguchi-Hanson instanton in gravity. The gauge field thus obtained represents an abelian-like object whose field is dipole-like at large distances, and which has no magnetic or electric charge.

hep-th↗

arXiv2018

Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond

In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called `exotic branes'---low codimension objects with highly non-perturbative tensions, scaling as $g_s^α$ for $α\leq -3$. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT)---collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string- and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist.

hep-th↗

arXiv2016

An Action for F-theory: $\mathrm{SL}(2) \times \mathbb{R}^+$ Exceptional Field Theory

We construct the 12-dimensional exceptional field theory associated to the group $\mathrm{SL}(2) \times \mathbb{R}^+$ . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus $\mathrm{SL}(2) \times \mathbb{R}^+$ exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism.

hep-th↗

arXiv2015

Strings, Branes and the Self-dual Solutions of Exceptional Field Theory

It has been shown that membranes and fivebranes are wave-like or monopole-like solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional Field Theory. This solution solves the twisted self-duality constraint. The 1/2 BPS brane spectrum, consisting of fundamental, solitonic and Dirichlet branes, in ten- and eleven-dimensional supergravity may all be extracted from this single solution of Exceptional Field Theory. The solution's properties such as the singularity structure and its asymptotic behaviour near the core and at infinity are investigated.

hep-th↗

arXiv2015

Branes are Waves and Monopoles

In a recent paper it was shown that fundamental strings are null waves in Double Field Theory. Similarly, membranes are waves in exceptional extended geometry. Here the story is continued by showing how various branes are Kaluza-Klein monopoles of these higher dimensional theories. Examining the specific case of the E7 exceptional extended geometry, we see that all branes are both waves and monopoles. Along the way we discuss the O(d; d) transformation of localized brane solutions not associated to an isometry and how true T-duality emerges in Double Field Theory when the background possesses isometries.

hep-th↗

arXiv2014

Duality Symmetric String and M-Theory

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E_{n(n)} U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.

hep-th↗

arXiv2014

Strings and Branes are Waves

We examine the equations of motion of double field theory and the duality manifest form of M-theory. We show the solutions of the equations of motion corresponding to null pp-waves correspond to strings or membranes from the usual spacetime perspective. A Goldstone mode analysis of the null wave solution in double field theory produces the equations of motion of the duality manifest string.

hep-th↗

arXiv2014

Global aspects of double geometry

We consider the concept of a generalised manifold in the O(d,d) setting, i.e., in double geometry. The conjecture by Hohm and Zwiebach for the form of finite generalised diffeomorphisms is shown to hold. Transition functions on overlaps are defined. Triple overlaps are trivial concerning their action on coordinates, but non-trivial on fields, including the generalised metric. A generalised manifold is an ordinary manifold, but the generalised metric on the manifold carries a gerbe structure. We show how the abelian behaviour of the gerbe is embedded in the non-abelian T-duality group. We also comment on possibilities and difficulties in the U-duality setting.

hep-th↗

arXiv2014

Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions

Previous constructions of supersymmetry for double field theory have relied on the so called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk-Schwarz reduction is imposed. The equivalence between the generalised Scherk-Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a byproduct we write the generalised Killing spinor equations for the supersymmetric double field theory.

hep-th↗

arXiv2013

The O_{D,D} Geometry of String Theory

We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the O_{D,D} structure. The connection is simultaneously torsionful and flat. Using this connection one may construct a proper covariant derivative for double field theory. We then write the doubled action in terms of the generalised torsion of this connection. This action then exactly reproduces that required for doubled field theory and gauged supergravity.

hep-th↗

arXiv2013

The Navier-Stokes equation and solution generating symmetries from holography

The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess solution-generating symmetries known as spacetime Ehlers transformations. These form a subgroup of the larger generalized Ehlers group acting on spacetimes with arbitrary matter content. We apply this generalized Ehlers group, in the presence of Killing isometries, to vacuum metrics with hydrodynamic duals to develop a formalism for solution-generating transformations of Navier-Stokes fluids. Using this we provide examples of a linear energy scaling from RG flow under vanishing vorticity, and a set of Z_2 symmetries for fixed viscosity.

hep-th↗

arXiv2012

The gauge structure of generalised diffeomorphisms

We investigate the generalised diffeomorphisms in M-theory, which are gauge transformations unifying diffeomorphisms and tensor gauge transformations. After giving an En(n)-covariant description of the gauge transformations and their commutators, we show that the gauge algebra is infinitely reducible, i.e., the tower of ghosts for ghosts is infinite. The Jacobiator of generalised diffeomorphisms gives such a reducibility transformation. We give a concrete description of the ghost structure, and demonstrate that the infinite sums give the correct (regularised) number of degrees of freedom. The ghost towers belong to the sequences of rep- resentations previously observed appearing in tensor hierarchies and Borcherds algebras. All calculations rely on the section condition, which we reformulate as a linear condition on the cotangent directions. The analysis holds for n < 8. At n = 8, where the dual gravity field becomes relevant, the natural guess for the gauge parameter and its reducibility still yields the correct counting of gauge parameters.

hep-th↗