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Jean-Loup Gervais

Publications and source records attributed to Jean-Loup Gervais.

At least 19 recordsLinked to original sources
arXiv2000

Integrable structures in classical off-shell 10D supersymmetric Yang-Mills theory

The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness conditions were proposed, which are explicitly integrable (hep-th/9811108), and are based on the breaking of symmetry SO(9,1) -> SO(2,1)xSO(7). In this article, we investigate their physical content. To this end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expansion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the spectrum including the original Yang-Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system to particular one-parameter families of light-like rays.

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arXiv1999

Backlund Transformations in 10D susy Yang-Mills Theories

This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A Bäcklund transformation is derived for the Yang type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten dimensional super Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the particular form of the equations is retained. These Yang type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This Bäcklund transformation is similar to the one proposed by A. Lesnov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.

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arXiv1999

Solution Generating in Ten Dimensional Supersymmetric Classical Yang--Mills Theories

In a recent paper (hep-th/9811108), Saveliev and the author showed that there exits an on-shell light cone gauge where the non-linear part of the field equations reduces to a (super) version of Yang's equations which may be solved by methods inspired by the ones previously developed for self-dual Yang-Mills equations in four dimensions. Later on (hep-th/9903218), the analogy between these latter theories and the present ones was pushed further by writing down a set of super partial linear differential equations which are the analogues of the Lax pair of Belavin and Zakharov. Using this Lax representation, it is shown in the present article that solution-generating techniques are at work, which are similar to the ones developed for four dimensional self-dual Yang-Mills theories in the late seventies.

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arXiv1999

Lax equations in ten dimensional supersymmetric classical Yang-Mills theories

In a recent paper (hep-th/9811108), Saveliev and the author showed that there exits an on-shell light cone gauge where the non-linear part of the field equations reduces to a (super) version of Yang's equations which may be solved by methods inspired by the ones previously developed for self-dual Yang-Mills equations in four dimensions. Here, the analogy between these latter theories and the present ones is pushed further by writing down a set of super partial linear differential equations whose consistency conditions may be derived from the SUSY Y-M equations in ten dimensions, and which are the analogues of the Lax pair of Belavin and Zakharov. On the simplest example of the two pole ansatz, it is shown that the same solution-generating techniques are at work, as for the derivation of the celebrated multi-instanton solutions carried out in the late seventies. The present Lax representation, however, is only a consequence of (instead of being equivalent to) the field equations, in contrast with the Belavin Zakharov Lax pair.

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arXiv1998

Progress in classically solving ten dimensional supersymmetric reduced Yang-Mills theories

It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to $(1+1)$ space-time dimensions, the general solution of this subset of equations is derived. The remaining non-linear equations are written in a form which is analogous to Yang equations, albeit with superderivatives involving sixteen fermionic coordinates. It is shown that this non-linear part may, nevertheless, be solved by methods similar to powerful technics previously developed for the (purely bosonic) self-dual Yang Mills equations in four dimensions.

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arXiv1998

T Duality Between Perturbative Characters of $E_8\otimes E_8$ and SO(32) Heterotic Strings Compactified On A Circle

Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier study of the type II case (hep-th/9707107), is the appearence of Wilson lines. Using SO(17,1) transformations between the weight lattices reveals the existence of an intermediate theory where T duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.

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arXiv1997

T Duality of Perturbative Characters for Closed Bosonic and Type II String Theories

The duality properties of perturbative string characters associated with the transverse space-time rotations are studied. T duality is achieved by suitably integrating over the total momentum, contrary to earlier discussions. The O(8) triality properties of the characters for critical superstrings, are derived. This shows the existence of a third formulation (unnoticed so far to our knowledge) equivalent to, but different from the ones of Neveu-Schwarz-Ramond, and Green-Schwarz. Projectors in the NS and R sectors are defined in the GS formalism. The consequences of supersymmetry are neatly derived at once for all massive states by factorising the character of the long SUSY multiplet.

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arXiv1996

Solving the strongly coupled 2D gravity III: String susceptibility and topological N-point functions

We spell out the derivation of novel features, put forward earlier in a letter, of two dimensional gravity in the strong coupling regime, at $C_L=7$, 13, 19. Within the operator approach previously developed, they neatly follow from the appearence of a new cosmological term/marginal operator, different from the standard weak-coupling one, that determines the world sheet interaction. The corresponding string susceptibility is obtained and found real contrary to the continuation of the KPZ formula. Strongly coupled (topological like) models--only involving zero-mode degrees of freedom--are solved up to sixth order, using the ward identities which follow from the dependence upon the new cosmological constant. They are technically similar to the weakly coupled ones, which reproduce the matrix model results, but gravity and matter quantum numbers are entangled differently.

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arXiv1996

On the Liouville coupling constants

For the general operator product algebra coefficients derived by Cremmer Roussel Schnittger and the present author with (positive integer) screening numbers, the coupling constants determine the factors additional to the quantum group 6j symbols. They are given by path independent products over a two dimensional lattice in the zero mode space. It is shown that the ansatz for the three point function of Dorn-Otto and Zamolodchikov-Zamolodchikov precisely defines the corresponding flat lattice connection, so that it does give a natural generalization of these coupling constants to continuous screening numbers. The consistency of the restriction to integer screening charges is reviewed, and shown to be linked with the orthogonality of the (generalized) 6j symbols. Thus extending this last relation is the key to general screening numbers.

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arXiv1995

Higher Grading Generalisations of the Toda Systems

In the present paper we obtain some integrable generalisations of the Toda system generated by flat connection forms taking values in higher ${\bf Z}$--grading subspaces of a simple Lie algebra, and construct their general solutions. One may think of our systems as describing some new fields of the matter type coupled to the standard Toda systems. This is of special interest in nonabelian Toda theories where the latter involve black hole target space metrics. We also give a derivation of our conformal system on the base of the Hamiltonian reduction of the WZNW model; and discuss a relation between abelian and nonabelian systems generated by a gauge transformation that maps the first grading description to the second. The latter involves grades larger than one.

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arXiv1994

From Weak to Strong Coupling in Two-Dimensional Gravity

The strong coupling physics of two dimensional gravity at C=7, 13, 19 is deciphered, by building up on previous works along the same line (for a recent review, of the background material, see hep-th/9408069). It is shown that chirality becomes deconfined. The string suceptibility is derived, and found to be real contrary to the continuation of the KPZ formula. Topological Liouville string theories (without transverse degree of freedom) are explicitely solved. Altough they involve strongly coupled gravity, they share many features with the standard matrix models.

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arXiv1994

Lotka--Volterra Type Equations and their Explicit Integration

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of $A_r$, $B_r$, $C_r$, and $G_2$ on the same footing.

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arXiv1994

Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields

We construct the exponentials of the Liouville field with continuous powers within the operator approach. Their chiral decomposition is realized using the explicit Coulomb-gas operators we introduced earlier. {}From the quantum-group viewpoint, they are related to semi-infinite highest or lowest weight representations with continuous spins. The Liouville field itself is defined, and the canonical commutation relations verified, as well as the validity of the quantum Liouville field equations. In a second part, both screening charges are considered. The braiding of the chiral components is derived and shown to agree with the ansatz of a parallel paper of J.-L. G. and Roussel: for continuous spins the quantum group structure $U_q(sl(2)) \odot U_{\qhat}(sl(2))$ is a non trivial extension of $U_q(sl(2))$ and $U_{\qhat}(sl(2))$. We construct the corresponding generalized exponentials and the generalized Liouville field.

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arXiv1994

Solving the Strongly Coupled 2D Gravity: 2. Fractional-Spin Operators, and Topological Three-Point Functions

Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study of the chiral bootstrap (recently completed by E. Cremmer, and the present authors) to the case of semi-infinite quantum-group representations which correspond to positive integral screening numbers. In particular, we prove the Bidenharn-Elliot and Racah identities for q-deformed 6-j symbols generalized to continuous spins. The decoupling of the family of physical chiral operators (with real conformal weights) at the special values C_{Liouville}= =7, 13, and 19, is shown to provide a full solution of Moore and Seiberg's equations, only involving operators with real conformal weights. Moreover, our study confirms the existence of the strongly coupled topological models. The three-point functions are shown to be given by a product of leg factors similar to the ones of the weakly coupled models. However, contrary to this latter case, the equality between the quantum group spins of the holomorphic and antiholomorphic components is not preserved by the local vertex operator. Thus the ``c=1'' barrier appears as connected with a deconfinement of chirality.

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arXiv1993

$W$--geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Plücker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding Kähler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Plücker embedding. These conditions are automatically fulfiled when Toda equations hold.

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arXiv1993

Introduction to Differential W-Geometry

Ideas recently put forward by Y. Matsuo and the author are summarized on the example of the simplest ($W_3$) generalization of two-dimensional gravity. These notes are based on lectures given at the workshop `` Strings, Conformal Models and Topological Field Theories'', Cargese 12-21 May 1993; and at the meeting ``String 93'', Berkeley, 24-29 May 1993.

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