arXiv subjects

Christopher N. Pope

Publications and source records attributed to Christopher N. Pope.

6 recordsLinked to original sources

arXiv2026

Mass and Force Relations for Extremal E2MD Black Holes

We study static extremal black holes in Einstein gravity coupled to a dilaton and two Maxwell fields with independent dilaton couplings $a$ and $b$. When $b=-1/a$ in four dimensions, a time-symmetric initial-value construction allows us to determine the masses and interaction energies of multi-black-hole configurations. On this special locus, the long-range force between any two extremal black holes vanishes. For arbitrary $a$ and $b$, a constant dilaton-shift symmetry, together with homogeneity and the extremality condition, yields a first-order ordinary differential equation that determines the extremal mass as a function of the two electric charges. This equation allows us to analyze the force between non-identical extremal black holes without having to know the explicit black-hole geometry. In all analytically controlled regimes that we examine, the locus $b=-1/a$ separates attractive behavior for $b>-1/a$ from repulsive behavior for $b<-1/a$. We extend the analysis to arbitrary spacetime dimensions, where the corresponding force-cancellation condition is $ab=-2(d-2)/(d-1)$. Finally, we test this sign pattern using the exact $A_2$, $B_2$ and $G_2$ Toda black holes. In the $G_2$ case, a potentially problematic branch is excluded because it contains naked singularities outside the horizon, suggesting an intriguing connection between regularity and the sign of long-range forces.

hep-th↗

arXiv2024

Consistent Truncations and Dualities

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in double field theory, which have been shown to be in one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation is only the tip of the iceberg. Currently, the most general known classes of T-dualities (excluding mirror symmetry) are based on dressing cosets. But as we discuss, they can be further extended to the even larger class of generalised cosets. We prove that the latter give rise to consistent truncations for which the ansatz can be constructed systematically. Hence, we pave the way for many new examples of T-dualities and consistent truncations. The arising structures result in covariant tensors with more than two derivatives and we argue how they might be key to understand generalised T-dualities and consistent truncations beyond the leading two derivative level.

hep-th↗

arXiv2024

Generalized Dualities and Supergroups

Using a recently developed formulation of double field theory in superspace, the graviton, $B$-field, gravitini, dilatini, and Ramond-Ramond bispinor are encoded in a single generalized supervielbein. Duality transformations are encoded as orthosymplectic transformations, extending the bosonic $O(D,D)$ duality group, and these act on all constituents of the supervielbein in an easily computable way. We first review conventional non-abelian T-duality in the Green-Schwarz superstring and describe the dual geometries in the language of double superspace. Since dualities are related to super-Killing vectors, this includes as special cases both abelian and non-abelian fermionic T-duality. We then extend this approach to include Poisson-Lie T-duality and its generalizations, including the generalized coset construction recently discussed in arXiv:1912.11036. As an application, we construct the supergeometries associated with the integrable $λ$ and $η$ deformations of the $AdS_5 \times S^5$ superstring. The deformation parameters $λ$ and $η$ are identified with the possible one-parameter embeddings of the supergravity frame within the doubled supergeometry. In this framework, the Ramond-Ramond bispinors are directly computable purely from the algebraic data of the supergroup.

hep-th↗

arXiv2024

Singular limits in STU supergravity

We analyse the STU sectors of the four-dimensional maximal gauged supergravities with gauge groups ${\rm SO(8)}$, ${\rm SO(6)}\ltimes\mathbb{R}^{12}$ and $[{\rm SO(6)}\times{\rm SO(2)}]\ltimes\mathbb{R}^{12}$, and construct new domain-wall black-hole solutions in $D=4$. The consistent Kaluza-Klein embedding of these theories is obtained using the techniques of Exceptional Field Theory combined with the 4$d$ tensor hierarchies, and their respective uplifts into $D=11$ and type IIB supergravities are connected through singular limits that relate the different gaugings.

hep-th↗

arXiv2023

Mass And Force Relations For Einstein-Maxwell-Dilaton Black Holes

We investigate various properties of extremal dyonic static black holes in Einstein-Maxwell-Dilaton theory. Using the fact that the long-range force between two identical extremal black holes always vanishes, we obtain a simple first-order ordinary differential equation for the black hole mass in terms of its electric and magnetic charges. Although this equation appears not to be solvable explicitly for general values of the strength a of the dilatonic coupling to the Maxwell field, it nevertheless provides a powerful way of characterising the black hole mass and the scalar charge. We make use of these expressions to derive general results about the long-range force between two non-identical extremal black holes. In particular, we argue that the force is repulsive whenever a>1 and attractive whenever a<1 (it vanishes in the intermediate BPS case a=1). The sign of the force is also correlated with the sign of the binding energy between extremal black holes, as well as with the convexity or concavity of the surface characterizing the extremal mass as a function of the charges. Our work is motivated in part by the Repulsive Force Conjecture and the question of whether long range forces between non-identical states can shed new light on the Swampland.

hep-th↗

arXiv2017

Beyond E11

We study the non-linear realisation of E11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.

hep-th↗