arXiv subjects

José M. Figueroa-O'Farrill

Publications and source records attributed to José M. Figueroa-O'Farrill.

6 recordsLinked to original sources

arXiv2026

The spectrum of the bosonic ambitwistor string revisited

We revisit the calculation of the spectrum of the bosonic ambitwistor string, understood as the BRST cohomology or, equivalently, as the semi-infinite cohomology of the $\mathrm{BMS}_3$ Lie algebra relative to the centre with values in a particular module. We work in momentum space, which allows us to work algebraically and interpret the BRST cohomology as inducing representations of the Poincaré group. In agreement with the existing literature, we find that all the cohomology resides in the massless sector, but a careful representation-theoretic analysis of the spectrum reveals, in addition to the usual massless sector of the closed bosonic string (dilaton, metric and Kalb--Ramond field), also a massless vector. We devote a large part of the paper to describing the cohomology at a massless momentum $p$ as a module over the stabiliser $H$ of $p$ in the Lorentz group, a task which is made difficult due to $H$ not acting reducibly when $p\neq 0$. This allows us to conclude that the spectrum is not unitary, forbidding the interpretation of the extra massless vector as a Maxwell field.

hep-th↗

arXiv2020

Constructing N=2 Superconformal Algebras out of N=1 Affine Lie Algebras

We study the problem of constructing N=2 superconformal algebras out of an N=1 affine Lie algebra. Following a recent independent observation of Getzler and the author, we derive a simplified set of N=2 master equations, which we then proceed to solve for the case of sl(2). There is a unique construction for all noncritical values of the level, which can be identified as the Kazama-Suzuki coset associated to the hermitian symmetric space SO(3)/SO(2). We also identify the construction with a generalized parafermionic construction or, after bosonization, with a bosonic construction of the type analyzed by Kazama and Suzuki. A mild generalization of this construction can be associated to any embedding of sl(2) in G.

hep-th↗

arXiv2020

Affine Algebras, $N{=}2$ Superconformal Algebras, and Gauged WZNW Models

We find a canonical $N{=}2$ superconformal algebra (SCA) in the BRST complex associated to any affine Lie algebra $\hat{\mathbf{h}}$ with $\mathbf{h}$ semisimple. In contrast with the similar known results for the Virasoro, $N{=}1$ supervirasoro, and $W_3$ algebras, this SCA does not depend on the particular "matter" representation chosen. Therefore it follows that every gauged WZNW model with data $(\mathbf{g}\supset\mathbf{h}, k)$ has an $N{=}2$ SCA with central charge $c=3\dim\mathbf{g}$ independent of the level $k$. In particular, this associates to every embedding $sl(2) \subset \mathbf{g}$ a one-parameter family of $c{=}9$ $N{=}2$ supervirasoro algebras. As a by-product of the construction, one can deduce a new set of "master equations" for generalized $N{=}2$ supervirasoro constructions which is simpler than the one considered thus far.

hep-th↗

arXiv2019

Conformal Lie algebras via deformation theory

We discuss possible notions of conformal Lie algebras, paying particular attention to graded conformal Lie algebras with $d$-dimensional space isotropy: namely, those with a $\mathfrak{co}(d)$ subalgebra acting in a prescribed way on the additional generators. We classify those Lie algebras up to isomorphism for all $d\geq 2$ following the same methodology used recently to classify kinematical Lie algebras, as deformations of the `most abelian' graded conformal algebra. We find 17 isomorphism classes of Lie algebras for $d\neq 3$ and 23 classes for $d=3$. Lie algebra contractions define a partial order in the set of isomorphism classes and this is illustrated via the corresponding Hesse diagram. The only metric graded conformal Lie algebras are the simple Lie algebras, isomorphic to either $\mathfrak{so}(d{+}1,2)$ or $\mathfrak{so}(d{+}2,1)$. We also work out the central extensions of the graded conformal algebras and study their invariant inner products. We find that central extensions of a Lie algebra in $d=3$ and two Lie algebras in $d=2$ are metric. We then discuss several other notions of conformal Lie algebras (generalised conformal, Schrödinger and Lifshitz Lie algebras) and we present some partial results on their classification. We end with some open problems suggested by our results.

hep-th↗

arXiv2018

Kinematical Lie algebras via deformation theory

We present a deformation theory approach to the classification of kinematical Lie algebras in 3+1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical Lie algebra and of its universal central extension, up to isomorphism. In addition we determine which of these Lie algebras admit an invariant symmetric inner product. Among the new results, we find some deformations of the centrally extended static kinematical Lie algebra which are extensions (but not central) of deformations of the static kinematical Lie algebra. This paper lays the groundwork for two companion papers which present similar classifications in dimension D + 1 for all D>3 and in dimension 2+1.

hep-th↗

arXiv2018

Higher-dimensional kinematical Lie algebras via deformation theory

We classify kinematical Lie algebras in dimension $D \geq 4$. This is approached via the classification of deformations of the relevant static kinematical Lie algebra. We also classify the deformations of the universal central extension of the static kinematical Lie algebra in dimension $D\geq 4$. In addition we determine which of these Lie algebras admit an invariant inner product.

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