arXiv subjects

Bernard Julia

Publications and source records attributed to Bernard Julia.

15 recordsLinked to original sources

arXiv2018

Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4D

After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining ${\cal N}=2$ pure supergravity as the only possibility. These results are obtained with the BRST-BV deformation method around the flat and (A)dS backgrounds in 4 dimensions. The same method applied to $n_{v}$ vectors, ${\cal N}$ real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields ${\cal N}=3$ pure supergravity as well as ${\cal N}=1$ pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently from the matter content, we finally derive strong necessary quadratic constraints on the possible gaugings for an arbitrary number of spin-1 and spin-3/2 gauge fields, that are relevant for larger supergravities.

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arXiv2018

Deformations of vector-scalar models

Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.

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arXiv2017

A note on "gaugings" in four spacetime dimensions and electric-magnetic duality

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions. Ignoring supersymmetry we consider in this paper $n_v$ abelian vector potentials in four spacetime dimensions with non-minimal kinetic coupling to $n_s$ uncharged (possibly nonlinear) scalar fields. As in the case of extended supergravities, one model may possess different formulations related by $Sp(2n_v,\mathbb{R})$. The symplectic group mixes its electric and magnetic potentials. The model admits a global duality symmetry subgroup $G$ which acts also on the scalars. We recall first how the general second order Lagrangian, its local deformations and those of its abelian gauge group will depend on the choice of $2n_v$ directions (choice of "Darboux frame"). We start from a general frame defined by the symplectic transformation relating it to a fixed"reference" one. Combinations of symplectic matrix coefficients appear then as constant parameters in the second order Lagrangians. Another gauging method uses an "embedding tensor" that characterizes the realization of the gauge group via the global duality group. It involves additional 2-form gauge fields. A suitable zero charge limit of this realization has abelian gauge group and the "gauging" can be viewed as a consistent deformation of that limit. We show that the two methods applied to the corresponding ungauged models have equivalent local deformations -- and more generally, have isomorphic local BRST cohomology at all ghost numbers. We finally consider manifestly duality invariant first order actions with abelian gauge group. We point out that obstructions to non-abelian deformations of the Yang-Mills type exhibited in a previous work remain present when couplings to scalar fields are included.

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arXiv2008

Gravitational duality near de Sitter space

Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic actions. The de Sitter action itself is found to be equivalent to a simple and natural quadratic action. In this paper we also describe explicitly the reparameterization and duality invariances of gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant doubling of the fields using the Hamiltonian formalism leads to first order time evolution with manifest duality symmetry. As a special case we recover the linear flat space result of Henneaux and Teitelboim by a smooth limiting process.

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arXiv2008

Magic N=2 supergravities from hyper-free superstrings

We show by explicit construction the existence of various four dimensional models of type II superstrings with N=2 supersymmetry, purely vector multiplet spectrum and no hypermultiplets. Among these, two are of special interest, at the field theory level they correspond to the two exceptional N=2 supergravities of the magic square that have the same massless scalar field content as pure N=6 supergravity and N=3 supergravity coupled to three extra vector multiplets. The N=2 model of the magic square that is associated to N=6 supergravity is very peculiar since not only the scalar degrees of freedom but all the bosonic massless degrees of freedom are the same in both theories. All presented hyper-free N=2 models are based on asymmetric orbifold constructions with N=(4,1) world-sheet superconformal symmetry and utilize the 2d fermionic construction techniques. The two exceptional N=2 models of the magic square are constructed via a "twisting mechanism" that eliminates the extra gravitini of the N=6 and N=3 extended supergravities and creates at the same time the extra spin-1/2 fermions and spin-1 gauge bosons which are necessary to balance the numbers of bosons and fermions. Theories of the magic square with the same amount of supersymmetry in three and five space-time dimensions are constructed as well, via stringy reduction and oxidation from the corresponding four-dimensional models.

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arXiv2004

Cosmological billiards and oxidation

We show how the properties of the cosmological billiards provide useful information (spacetime dimension and $p$-form spectrum) on the oxidation endpoint of the oxidation sequence of gravitational theories. We compare this approach to the other available methods: $GL(n,R)$ subgroups and the superalgebras of dualities.

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arXiv2004

Superfield T-duality rules

A geometric treatment of T-duality as an operation which acts on differential forms in superspace allows us to derive the complete set of T-duality transformation rules which relate the superfield potentials of D=10 type IIA supergravity with those of type IIB supergravity including Ramond-Ramond superfield potentials and fermionic supervielbeins. We show that these rules are consistent with the superspace supergravity constraints.

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arXiv2004

Superfield T-duality rules in ten dimensions with one isometry

In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T-duality and discuss the main steps of our approach to the derivation of the superfield T-duality rules, including the treatment of T-duality as an operation acting on differential forms rather than on the superspace coordinates.

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arXiv2003

Real Borcherds Superalgebras and M-theory

The correspondence between del Pezzo surfaces and field theory models over the complex numbers or for split real forms is extended to other real forms, in particular to those compatible with supersymmetry. Specifically, all theories of the Magic triangle that reduce to the pure supergravities in four dimensions correspond to singular real del Pezzo surfaces and the same is true for the Magic square of N=2 SUGRAS. A real del Pezzo surface is the invariant set under an antilinear involution of a complex one. This conjugation induces an involution of the Picard group that preserves the anticanonical class and the intersection form. The known non-split U-duality algebras are embedded into superBorcherds algebras defined by their Cartan matrix (minus the intersection form) and fixed by the anti-involution. These data may be described by Tits-Satake bicoloured diagrams. As in the split case, oxidation results from blowing down disjoint real P^1's of self-intersection -1. The singular del Pezzo surfaces of interest are obtained by degenerating regular surfaces upon contraction of real curves of self-intersection -2. We use the finite classification of real simple singularities to exhibit the relevant normal surfaces. We also give a general construction of more magic triangles like a type I split magic triangle and prove their (approximate) symmetry with respect to their diagonal, this symmetry argument was announced in our previous paper for the split case.

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arXiv2003

Hyperbolic billiards of pure D=4 supergravities

We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz (BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find that just as for the cases N=0 and N=8 investigated previously, these billiards can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature arises, however, which is that the relevant Kac-Moody algebra can be the Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of this property is provided by showing that the data relevant for determining the billiards are the restricted root system and the maximal split subalgebra of the finite-dimensional real symmetry algebra characterizing the toroidal reduction to D=3 spacetime dimensions. To summarize: split symmetry controls chaos.

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arXiv2003

Symmetries in M-theory: Monsters, Inc

We will review the algebras which have been conjectured as symmetries in M-theory. The Borcherds algebras, which are the most general Lie algebras under control, seem natural candidates.

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arXiv2002

On covariant phase space methods

It is well known that the Lagrangian and the Hamiltonian formalisms can be combined and lead to "covariant symplectic" methods. For that purpose a "pre-symplectic form" has been constructed from the Lagrangian using the so-called Noether form. However, analogously to the standard Noether currents, this symplectic form is only determined up to total divergences which are however essential ingredients in gauge theories. We propose a new definition of the symplectic form which is covariant and free of ambiguities in a general first order formulation. Indeed, our construction depends on the equations of motion but not on the Lagrangian. We then define a generalized Hamiltonian which generates the equations of motions in a covariant way. Applications to Yang-Mills, general relativity, Chern-Simons and supergravity theories are given. We also consider nice sets of possible boundary conditions that imply the closure and conservation of the total symplectic form. We finally revisit the construction of conserved charges associated with gauge symmetries, from both the "covariant symplectic" and the "covariantized Regge-Teitelboim" points of view. We find that both constructions coincide when the ambiguity in the Noetherian pre-symplectic form is fixed using our new prescription. We also present a condition of integrability of the equations that lead to these quantities.

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arXiv2002

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.

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arXiv2001

Hyperbolic Kac-Moody Algebras and Chaos in Kaluza-Klein Models

Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinsky, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike ("cosmological") singularity disappears in spacetime dimensions $D= d+1>10$. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this letter, we show that the same connection applies to pure gravity in any spacetime dimension $\geq 4$, where the relevant algebras are $AE_d$. In this way the disappearance of chaos in pure gravity models in $D > 10$ dimensions becomes linked to the fact that the Kac-Moody algebras $AE_d$ are no longer hyperbolic for $d > 9$.

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arXiv1999

Counterterms in type I Supergravities

We compute the one-loop divergences of D=10, N=1 supergravity and of its reduction to D=8. We study the tensor structure of the counterterms appearing in D=8 and D=10 and compare these to expressions previously found in the low energy expansion of string theory. The infinities have the primitive Yang-Mills tree amplitude as a common factor.

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