1,721,073 research outputs found
TWISTED N=2 SUPERGRAVITY AS TOPOLOGICAL GRAVITY IN 4 DIMENSIONS
No full textWe show that the BRST quantum version of pure D = 4 N = 2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions. The topological BRST complex is just a re-arrangement of the old BRST complex, that partly modifies the role of physical and ghost fields: indeed, the new ghost number turns out to be the sum of the old ghost number plus the internal U(1) charge. Furthermore, the action of N = 2 supergravity is retrieved from topological gravity by choosing a gauge fixing that reduces the space of physical states to the space of gravitational instanton configurations, namely to self-dual spin connections. The descent equations relating the topological observables are explicitly exhibited and discussed. Ours is a first step in a programme that aims at finding the topological sector of matter coupled N = 2 supergravity, viewed as the effective lagrangian of type II superstrings and, as such, already related two-dimensional topological field theories. As it stands the theory we discuss may prove useful in describing gravitational instanton moduli-spaces
GAUGED HYPERINSTANTONS AND MONOPOLE EQUATIONS
No full textThe monopole equations in the dual abelian theory of the N = 2 gauge-theory, recently proposed by Witten as a new tool to study topological invariants, are shown to be the simplest elements in a class of instanton equations that follow from the improved topological twist mechanism introduced by the authors in previous papers. When applied to the N = 2 sigma-model, this twisting procedure suggested the introduction of the so-called hyperinstantons that are the solutions to an appropriate condition of triholomorphicity imposed on the maps q : M --> N from a four-dimensional almost quaternionic world-manifold M to an almost quatemionic target manifold N. When gauging the sigma-model by coupling it to the vector multiplet of a gauge group G, one gets instantonic conditions (named by us gauged hyperinstantons) that reduce to the Seiberg-Witten equations for M = N = R(4) and G = U(1). The deformation of the self-duality condition on the gauge-field strength due to the monopole-hyperinstanton is very similar to the deformation of the self-duality condition on the Riemann curvature previously observed by the authors when the hyperinstantons are coupled to topological gravity. In this paper the general form of the hyperinstantonic equations coupled to both gravity and gauge multiplets is presented
TOPOLOGICAL TWIST IN 4 DIMENSIONS, R-DUALITY AND HYPERINSTANTONS
No full textIn this paper we continue the programme of topologically twisting N = 2 theories in D = 4, focusing on the coupling of vector multiplets to N = 2 supergravity. We show that in the minimal case, namely when the special geometry prepotential F(X) is a quadratic polynomial, the theory has a so far unknown on-shell U(1) symmetry, that we name R-duality. R-duality is a generalization of the chiral-dual on-shell symmetry of N = 2 pure supergravity and of the R-symmetry of N = 2 super Yang-Mills theory. Thanks to this, the theory can be topologically twisted and topologically shifted, precisely as pure N = 2 supergravity, to yield a natural coupling of topological gravity to topological Yang-Mills theory. The gauge-fixing condition that emerges from the twisting is the self-duality condition on the gauge field strength and on the spin connection. Hence our theory reduces to intersection theory in the moduli-space of gauge instantons living in gravitational instanton backgrounds. We remark that, for deep properties of the parent N = 2 theory, the topological Yang-Mills theory we obtain by taking the flat space limit of our gravity-coupled lagrangian is different from the Donaldson theory constructed by Witten. Whether this difference is substantial and what its geometrical implications may be is yet to be seen. We also discuss the topological twist of the hypermultiplets leading to topological quaternionic sigma-models- The instantons of these models, named by us hyperinstantons, correspond to a notion of triholomorphic mappings discussed in the paper. In all cases the new ghost number is the sum of the old ghost number plus the R-duality charge. The observables described by the theory are briefly discussed. In conclusion, the topological twist of the complete N = 2 theory defines intersection theory in the moduli-space of gauge instantons plus gravitational instantons plus hyperinstantons. This is possibly a new subject for further mathematical investigation
TOPOLOGICAL SIGMA-MODELS IN 4 DIMENSIONS AND TRIHOLOMORPHIC MAPS
No full textIt is well known that topological sigma-models in two dimensions constitute a path-integral approach to the study of holomorphic maps from a Riemann surface SIGMA to an almost complex manifold K, the most interesting case being that were K is a Kahler manifold. We show that, in the same way, topological sigma-models in four dimensions introduce a path-integral approach to the study of triholomorphic maps q: M --> N between a four-dimensional riemannian manifold M and an almost quaternionic manifold N. The most interesting cases are those where M, N are hyper-Kahler or quaternionic Kahler. BRST-cohomology translates into intersection theory in the moduli-space of this new class of instantonic maps, that are named hyperinstantons by us. The definition of triholomorphicity that we propose is expressed by the equation q - J(u) . q . j(u) = 0, where {j(u), u = 1, 2, 31 is an almost quaternionic structure on M and {J(u), u = 1, 2, 3) is an almost quaternionic structure on N. This is a generalization of the Cauchy-Fueter equations. For M, N hyper-Kahler, this generalization naturally arises by obtaining the topological sigma-model as a twisted version of the N = 2 globally supersymmetric sigma-model. We discuss various examples of hyperinstantons, in particular on the torus and the K3 surface. We also analyze the coupling of the topological sigma-model to topological gravity. The classification of triholomorphic maps and the analysis of their moduli-space is a new and fully open mathematical problem that we believe deserves the attention of both mathematicians and physicists
Integrable Scalar Cosmologies I. Foundations and links with String Theory
No full textWe build a number of integrable one-scalar spatially flat cosmologies, which play a natural role in inflationary
scenarios, examine their behavior in several cases and draw from them some general lessons
on this type of systems, whose potentials involve combinations of exponential functions, and on similar
non-integrable ones. These include the impossibility for the scalar to emerge from the initial singularity
descending along asymptotically exponential potentials with logarithmic slopes exceeding a critical value
(“climbing phenomenon”) and the inevitable collapse in a Big Crunch whenever the scalar tries to settle
at negative extrema of the potential. We also elaborate on the links between these types of potentials and
“brane supersymmetry breaking”, a mechanism that ties together string scale and scale of supersymmetry
breaking in a class of orientifold models
Hyperinstantons, the beltrami equation, and triholomorphic maps
No full textWe consider the Beltrami equation for hydrodynamics and we show that its solutions can be viewed as instanton solutions of a more general system of equations. The latter are the equations of motion for an N = 2 sigma model on 4-dimensional worldvolume (which is taken locally HyperK ̈ahler) with a 4-dimensional HyperK ̈ahler target space. By means of the 4D twisting procedure originally introduced by Witten for gauge theories and later generalized to 4D sigma- models by Anselmi and Fr ́e, we show that the equations of motion describe triholomophic maps between the worldvolume and the target space. Therefore, the classification of the solutions to the 3-dimensional Beltrami equation can be performed by counting the triholomorphic maps. The counting is easily obtained by using several discrete symmetries. Finally, the similarity with holomorphic maps for N = 2 sigma on Calabi-Yau space prompts us to reformulate the problem of the enumeration of triholomorphic maps in terms of a topological sigma model
Seven Lectures On The Group Manifold Approach To Supergravity And The Spontaneous Compactification Of Extra Dimensions
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