N=2 super Yang-Mills theory in projective superspace

We constructN=2 Yang-Mills theory in projective superspace by exploiting the analogy to Ward's twistor construction of self-dual Yang-Mills fields.Work supported in part by NSF grant No. PHY 85-07627     

Super-Toda theories and W-algebras from superspace Wess-Zumino-Witten models

Using a superspace approach, it is proved that aN=1 Super-Toda theory can be seen as a constrained WZW model based on a supergroup. The gauge transformations which survive the constraints are then usedà la Drinfeld Sokolov to determine explicity the super-W algebra underlying this theory. The conformal spin content of any such super-Walgebra is provided in the general case.URA 14-36 du CNRS, associée à l'E.N.S. de Lyon, et au L.A.P.P.     

Gauge-invariant sigma models in N=2 superspace

We construct a new broad class of gauge-invariant nonlinear sigma models in N=2 superspace. The dimensional reduction of the theories obtained to d=2 leads to N=4 nonlinear sigma models which are devoid of ultraviolet divergence in all orders of perturbation theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1989.     

Gauging N = 2 sigma models in harmonic superspace

We construct the general minimal coupling of N = 2 Yang-Mills fields to N = 2 sigma models in flat and curved harmonic superspace. We show that the complete symmetry group of the matter action can always be gauged in curved space. In flat space, we find that the gauging can be blocked by a local obstruction. We give a number of examples based on homogeneous quaternionic spaces and on quaternionic generalizations of the Taub-NUT and Eguchi-Hanson metrics.     

On holomorphic factorization of WZW and coset models

It is shown how coupling to gauge fields can be used to explain the basic facts concerning holomorphic factorization of the WZW model of two dimensional conformal field theory, which previously have been understood primarily by using conformal field theory Ward identities. We also consider in a similar vein the holomorphic factorization ofG/H coset models. We discuss theG/G model as a topological field theory and comment on a conjecture by Spiegelglas.Research supported in part by NSF Grant PHY86-20266     

Massive nonlinear sigma models and BPS domain walls in harmonic superspace

Four-dimensional massive nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kähler analog of the Kähler potential in theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kähler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi–Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi–Hanson limit.     

Supertwistors and superspace

In the paper the usual correspondence between twistors and geometrical objects in the Minkowski space is generalized to the supertwistor case by means of flag supermanifolds. This supertwistor correspondence is treated in detail. Chiral and non-chiral superspaces are constructed and their properties studied by means of supertwistors.     

The Witten index in superspace,two-dimensional superanomaly in Yang-Mills and gravitational background,and superspace Schwinger-Dewitt heat kernel method

We consider the Witten index in superspace and show that it is closely related to the superspace Schwinger-DeWitt heat kernel. By evaluating the Witten index for the two-dimensional superspace Yang-Mills and gravitational systems we obtain the two-dimensional superanomaly in an efficient way. Furthermore we show an effective way to treat the three-dimensional supersymmetric Yang-Mills system by the superspace Schwinger-DeWitt heat kernel method. As a consequence, the supersymmetric Chern-Simons term is obtained.     

Invariant*-products of holomorphic functions on the hyperbolic hermitian spaces

In this paper, we give an explicit basis of the invariant bidifferential operators on the Hermitian symmetric spaces of rank 1. As an application we prove that on noncompact Hermitian symmetric spaces of rank 1, an invariant^*-product coincides with the usual product for holomorphic functions.Aspirant du Fonds National Belge de la Recherche Scientifique.     

Supergravity with and without superspace

We show that the superspace formalism follows from the component formalism. After constructing the supervielbeins and superconnections off-shell in second-order formalism with the minimal set of auxiliary fields, we show that the resulting supertorsions satisfy the constraints of the various equivalent superspace approaches.     

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.     

A holomorphic and background independent partition function for matrix models and topological strings

We study various properties of a nonperturbative partition function which can be associated with any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix integrals over all possible filling fractions, and includes all the multi-instanton corrections to the perturbative 1/N$1/N$ expansion. We show that the nonperturbative partition function, which is manifestly holomorphic, is also modular and background independent: it transforms as the partition function of a twisted fermion on the spectral curve. Therefore, modularity is restored by nonperturbative corrections. We also show that this nonperturbative partition function obeys the Hirota equation and provides a natural nonperturbative completion for topological string theory on local Calabi–Yau 3-folds.     

Multicentre metrics and harmonic superspace

We develop a procedure for constructing a possible harmonic superspace lagrangian for any d = 4 multicentre metric and show that the lagrangians leading to such metrics are characterized by the existence of a U(1) of Pauli-Gursey invariance. As an application, the mixed Eguchi-Hanson-Taub-NUT metric is shown, by explicit calculations, to be the double Taub-NUT metric.     

点电荷、线电荷、面电荷模型的电荷体分布函数

利用δ函数,导出了点电荷、线电荷和面电荷模型在直角坐标、球坐标和柱坐标下的电荷体分布函数表达式,对处理一些具体的物理问题时十分有用。     

Functional integral and the Feynman-Kac formula in superspace

We consider the Cauchy problem for linear pseudodifferential equations in superspace. The solution is constructed in the form of series. It may be regarded as a definition of a chronological exponent of a pseudodifferential operator symbol and interpreted as a functional integral in superspace.