Searcharxiv⌕ Search

arXiv subjects

Laurent Baulieu

Publications and source records attributed to Laurent Baulieu.

At least 37 records · Page 2Linked to original sources
arXiv2010

SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry

The N=1,d=10 superYang-Mills action is constructed in a twisted form, using SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q derive from a Chern-Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)<SO(10)$ invariant decomposition, the N=1, d=10 theory is determined by only 6 supersymmetry generators, as in the twisted N=4, d=4 theory. There is a superspace with 6 twisted fermionic directions, with solvable constraints.

hep-th↗
arXiv2009

N=4 Yang--Mills theory as a complexification of the N=2 theory

A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant longitudinal components for the imaginary part of the gauge field. The latter becomes the vector field of the thirdly twisted $\N=4$ theory. Eventually, one gets a one to one correspondence between the fields of both theories. Analogous complexifications can be done for topological 2d-gravity and topological sigma models.

hep-th↗
arXiv2008

Supersymmetric Adler-Bardeen anomaly in N=1 super-Yang-Mills theories

We provide a study of the supersymmetric Adler--Bardeen anomaly in the $\N=1, d=4,6,10$ super-Yang--Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov--Taylor identities can be independently set for both gauge invariance and supersymmetry. We find a method with improved descent equations for getting the solutions of the consistency conditions of both Slavnov--Taylor identities and finding the local field polynomials for the standard Adler--Bardeen anomaly and its supersymmetric counterpart. We give the explicit solution for the ten-dimensional case.

hep-th↗
arXiv2008

Holomorphic Superspace

We give a twisted holomorphic superspace description for the super-Yang-Mills theory, using holomorphic and antiholomorphic decompositions of twisted spinors. We consider the case of the N=1 super-Yang-Mills theory in four dimensions. We solve the constraints in two different manners, without and with a prepotential. This might have further application for an holomorphic superspace description of N=1,d=10 theory. We also explain how the N=1 and N=2 holomorphic superspaces are related.

hep-th↗
arXiv2008

Twisted Superspace

We formulate the ten-dimensional super-Yang-Mills theory in a twisted superspace with 8+1 supercharges. Its constraints do not imply the equations of motion and we solve them. As a preliminary step for a complete formulation in a twisted superspace, we give a superspace path-integral formulation of the N=2, d=4 super-Yang-Mills theory without matter. The action is the sum of a Chern--Simons term depending on a super-connection plus a BF-like term. The integration over the superfield B implements the twisted superspace constraints on the super-gauge field, and the Chern-Simons action reduces to the known action in components.

hep-th↗
arXiv2008

Shadow Fields and Local Supersymmetric Gauges

To control supersymmetry and gauge invariance in super-Yang-Mills theories we introduce new fields, called shadow fields, which enable us to enlarge the conventional Faddeev-Popov framework and write down a set of useful Slavnov-Taylor identities. These identities allow us to address and answer the issue of the supersymmetric Yang-Mills anomalies, and to perform the conventional renormalization programme in a fully regularization-independent way.

hep-th↗
arXiv2008

Finiteness Properties of the N=4 Super-Yang--Mills Theory in Supersymmetric Gauge

With the introduction of shadow fields, we demonstrate the renormalizability of the N=4 super-Yang--Mills theory in component formalism, independently of the choice of UV regularization. Remarkably, by using twisted representations, one finds that the structure of the theory and its renormalization is determined by a subalgebra of supersymmetry that closes off-shell. Starting from this subalgebra of symmetry, we prove some features of the superconformal invariance of the theory. We give a new algebraic proof of the cancellation of the $β$ function and we show the ultraviolet finiteness of the 1/2 BPS operators at all orders in perturbation theory. In fact, using the shadow field as a Maurer--Cartan form, the invariant polynomials in the scalar fields in traceless symmetric representations of the internal R-symmetry group are simply related to characteristic classes. Their UV finiteness is a consequence of the Chern--Simons formula.

hep-th↗
arXiv2008

Shadows and Twisted Variables

We explain how a new type of fields called shadows and the use of twisted variables allow for a better description of Yang-Mills supersymmetric theories. (Based on lectures given in Cargese, June 2006.)

hep-th↗
arXiv2008

Reconstruction of N=1 supersymmetry from topological symmetry

The scalar and vector topological Yang-Mills symmetries on Calabi-Yau manifolds geometrically define consistent sectors of Yang-Mills D=4,6 N=1 supersymmetry, which fully determine the supersymmetric actions up to twist. For a CY_2 manifold, both N=1,D=4 Wess and Zumino and superYang-Mills theory can be reconstructed in this way. A superpotential can be introduced for the matter sector, as well as the Fayet-Iliopoulos mechanism. For a CY_3 manifold, the N=1, D=6 Yang-Mills theory is also obtained, in a twisted form. Putting these results together with those already known for the D=4,8 N=2 cases, we conclude that all Yang--Mills supersymmetries with 4, 8 and 16 generators are determined from topological symmetry on special manifolds.

hep-th↗
arXiv2008

New Results on N=4 SuperYang-Mills Theory

The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \times SU(2) \subset SL(2,R) \times SU(2) internal symmetry and two scalar and one vector BRST topological symmetry operators. This determines an off-shell closed sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully determine the theory, in a Lorentz covariant way. This reduced algebra derives from horizontality conditions in four dimensions. The horizontality conditions only depend on the geometry of the Yang-Mills fields. They also descend from a genuine horizontality condition in eight dimensions. In fact, the SL(2,R) symmetry is induced by a dimensional reduction from eight to seven dimensions, which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs by dimensional reduction from seven to four dimensions. When the four dimensional manifold is hyperKahler, one can perform a twist operation that defines the N=4 supersymmetry and its SL(2,H)\sim SU(4) R-symmetry in flat space. (For defining a TQFT on a more general four manifold, one can use the internal SU(2)-symmetry and redefine a Lorentz SO(4) invariance). These results extend in a covariant way the light cone property that the N=4 SuperYang-Mills theory is actually determined by only 8 independent generators, instead of the 16 generators that occur in the physical representation of the superPoincare algebra. The topological construction disentangles the off-shell closed sector of the (twisted) maximally supersymmetric theory from the (irrelevant) sector that closes only modulo equations of motion. It allows one to escape the question of auxiliary fields in N=4 SuperYang-Mills theory.

hep-th↗
arXiv2008

Supersymmetric renormalization prescription in N = 4 super-Yang--Mills theory

Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry.

hep-th↗
arXiv2008

Ten-dimensional super-Yang-Mills with nine off-shell supersymmetries

After adding 7 auxiliary scalars to the d=10 super-Yang-Mills action, 9 of the 16 supersymmetries close off-shell. In this paper, these 9 supersymmetry generators are related by dimensional reduction to scalar and vector topological symmetry in $\N$=2 d=8 twisted super-Yang-Mills. Furthermore, a gauge-invariant superspace action is constructed for d=10 super-Yang-Mills where the superfields depend on 9 anticommuting theta variables.

hep-th↗
arXiv2008

Topological Vector Symmetry of BRSTQFT and Construction of Maximal Supersymmetry

The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting "equivariant topological field theory" corresponds to the twist of super Yang-Mills theory on Omega backgrounds.

hep-th↗
arXiv2008

Superconformal invariance from N=2 supersymmetry Ward identities

We algebraically prove the cancellation of the beta function at all order of perturbation theory of N=2 supersymmetric gauge theories with a vanishing one-loop beta function. The proof generalises that recently given for the N=4 case. It uses the consistent Slavnov-Taylor identities of the shadow dependent formulation. We also demonstrate the cancellation at all orders of the anomalous dimensions of vector and hypermultiplet one half BPS operators.

hep-th↗
arXiv2005

Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds

We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT's (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.

hep-th↗
arXiv2003

Gravitational Topological Quantum Field Theory Versus N = 2 D = 8 Supergravity and its lift to N = 1 D = 11 Supergravity

In a previous work, it was shown that the 8-dimensional topological quantum field theory for a metric and a Kalb-Ramond 2-form gauge field determines N = 1 D = 8 supergravity. It is shown here that, the combination of this TQFT with that of a 3-form determines N = 2 D = 8 supergravity, that is, an untruncated dimensional reduction of N = 1 D = 11 supergravity. Our construction holds for 8-dimensional manifolds with Spin(7) \subset SO(8) holonomy. We suggest that the origin of local Poincare supersymmetry is the gravitational topological symmetry. We indicate a mechanism for the lift of the TQFT in higher dimensions, which generates Chern-Simons couplings.

hep-th↗
arXiv2003

Supergravity and the Knitting of the Kalb--Ramond Two-Form in Eight-Dimensional Topological Gravity

Topological euclidean gravity is built in eight dimensions for manifolds with $Spin(7) \subset SO(8)$ holonomy. In a previous work, we considered the construction of an eight-dimensional topological theory describing the graviton and one graviphoton. Here we solve the question of determining a topological model for the combined system of a metric and a Kalb--Ramond two-form gauge field. We then recover the complete $N=1, D=8$ supergravity theory in a twisted form. We observe that the generalized self-duality conditions of our model correspond to the octonionic string equations.

hep-th↗