Self-Dual Conformal Supergravity and the Hamiltonian Formulation

In terms of Dirac matrices the self-dual and anti-self-dual decomposition of conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variables include the self-dual spin connection i.e. the Ashtekar connection rather than the triad. The Hamiltonian formulation and the constraints are obtained by using the Dirac-Bergmann algorithm.     

The Green-Schwarz superstring σ-model

We study the Green-Schwarz superstring coupled to a ten-dimensional supergravity background. We exhibit the background and quantum invariances of the action expanded in terms of normal coordinates. In the presence of nontrivial fermionic background we go to components and identity the vertex operators for emitting the physical supergravity fields. A comparison with the Neveu-Schwarz-Ramond formalism is then obtained by going to light-cone gauge.     

SU(2) Charges as Angular Momentum in N = 1 Self-Dual Supergravity

The N = 1 self-dual supergravity has SL(2, ) symmetry. This symmetry results inSU(2) charges as the angular momentum. As innonsupersymmetric self-dual gravity, the currents arealso of their potentials and are therefore identically conserved. Thecharges are generally invariant and gauge covariantunder local SU(2) transforms and approach being rigid atspatial infinity. The Poisson brackets constitute the su(2) algebra and hence can be interpretedas the generally covariant conservative angularmomentum.     

Gauge fields and D-branes

We prove that self-dual gauge fields in type I superstring theory are equivalent to configurations of Dirichlet 5-branes, by showing that the world-sheet theory of a Dirichlet 1-brane moving in a background of 5-branes includes an “ADHM sigma model”. This provides an explicit construction of the equivalent self-dual gauge field. We also discuss type II.     

Radiative corrections to the effective potential inN=1 supergravity

We compute the one loop quadratic divergences to the effective potential of the matter scalars inN=1 supergravity. We discuss in some special instances (the Das-Freedman and the Deser-Zumino Lagrangians) the problem of supersymmetry gauge invariance. We comment on the relevance of the calculation to model building.     

Gauge quantization for spin-32 fields

The free massless Rarita-Schwinger equation and a recently constructed interacting field theory known as supergravity are invariant under fermionic gauge transformations. Gauge field quantization techniques are applied in both cases. For the free field the Faddeev-Popov ansatz for the generating functional is justified by showing that it is equivalent to canonical quantization in a particular gauge. Propagators are obtained in several gauges and are shown to be ghost-free and causal. For supergravity the Faddeev-Popov ansatz is presented and the gauge fixing and determinant terms are discussed in detail in a Lorentz covariant gauge. The Slavnov-Taylor identity is obtained. It is argued that supergravity theory is free from the difficulty of acausal wave propagation of the type found by Velo and Zwanziger and that pole residues in tree approximation S-matrix elements are positive as required by unitarity.     

Local functional measure for some theories with singular Lagrangians

Local functional measure is calculated from the requirement of cancellation of the leading divergences at one loop level for gravity, supergravity and gravity-Yang-Mills theory.     

Einstein Supergravity and New Twistor String Theories

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N = 8 supergravity, another with the spectrum of N = 4 supergravity coupled to N = 4 super-Yang-Mills, and a family with N ≥ 0 supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N = 0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N = 8 and N = 4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.     

一种自对偶理论的规范不变形式及其量子化

对于一种新提出的自对偶场与规范场耦合的拉氏理论,本文给出相应的单上闭链,即Wess-Zumino项,构造了这种理论的规范不变的形式。利用正则量子化方法并通过选取适当的规范固定条件,证明了这规范不变的形式等价于原来的规范非不变的形式。此外,利用Batalin-Fradkin-Vilkovisky量子化方法,进一步指出这种等价性与规范固定条件的选择是无关的。 关键词：     

The auxiliary field structure in chirally extended supergravity

The auxiliary fields for Einstein supergravity with axial gauge coupling are those of Maxwell-Einstein supergravity. The gauge algebra is an irreducible extension of the gauge algebra of Einstein supergravity, so that the complete system is a gauge theory with an extra local chiral invariance, rather than a matter coupling.     

Radiative Corrections to Non-Abelian Gauge Theory in Homogeneous Self-Dual Backgrounds

We study the Euclidean version of non-Abelian gauge theories in homogeneous background fields with due regard of negative and zero modes of the gauge field kernel. For general gauge group and general background but without external currents we prove a relation between the propagators belonging to different gauge fixings. Specializing to a self-dual homogeneous background we derive nonperturbatively the propagators. Next we calculate the matter field contribution to the renormalized polarization tensor using a modified dimensional regularization scheme. We prove the validity of a modified Ward identity.     

Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity

Using the Dirac matrices the double self-dual and anti-self-dual structure of N=1 supergravity is discussed. It is shown that the (anti-)self-dual part of the curvature does not consist of the (anti-)self-dual part of the connection alone, and the (anti-)self-dual part of the Lagrangian quadratic in the curvature consists of the (anti-)self-dual part of the curvature alone only when the Lagrangian does not include torsion terms if the torsion of the spacetime does not vanish. Such a new Lagrangian is constructed. It includes no Einstein-Hilbert term but its self-dual part contains an Ashtekar term.     

Classical versus quantum trace for supersymmetric gauge fields

I calculate the effective action for a supersymmetric Schwinger model in a two-dimensional supergravity background and prove that the gauge superfield does not contribute to the trace anomaly in spite of its classical Weyl non-invariance.     

Superpotentials for Gauge and Conformal Supergravity Backgrounds

Effective superpotentials obtained by integrating out matter in super Yang-Mills and conformal supergravity backgrounds in SUSY theories are considered. The pure gauge and supergravity contributions (generalizing Veneziano-Yankielowicz terms) are derived by considering the case with matter fields in the fundamental representation of the gauge group. These contributions represent quantum corrections to the tree-level Yang-Mills and conformal supergravity actions. The classical equations of motion following from the conformal supergravity action require the background to be (super)conformally flat. This condition is unchanged by quantum corrections to the effective superpotential, irrespective of the matter content of the theory.     

The heterotic string and the geometry of the supersymmetric Einstein-Yang-Mills background

It is shown that the Wess-Zumino term of a heterotic superstring in aN = 1,D = 10 supergravity background can be given in terms of the torsion of the background in both versions (IA and IB) of theN = 1,D = 10 supergravity theory. The gauge degrees of freedom of the background are included according to the ideas of Kaluza and Klein. Explicit expressions for the vielbein, connection, torsion, and curvature of a space with 506 bosonic and 16 fermionic coordinates are given.     

Self-dual supergravity from N = 2 strings

A new heterotic N = 2 string with manifest target space supersymmetry is constructed by combining a conventional N = 2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma mode] is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in t', all in superspace. The resulting field equations describe N = 1 self-dual supergravity.     

Zeta-function regularization and multi-instanton determinants

The determinant of the covariant laplacian is discussed using the ζ-function regularization procedure. For a self-dual solution to a general euclidean Yang-Mills gauge theory, an integral expression for its variation, with respect to the parameters of the solution, is obtained in terms of the general construction of Atiyah et al. The conformal properties are analyzed and an explicit expression is obtained for a part of the determinant containing all the non-trivial behavior. The remaining conformally invariant part has not been determined. The removal of the infrared divergences by considering the problem on a sphere is discussed in some detail.     

Infrared divergences and a non-local gauge for superspace Yang-Mills theory

The usual superspace approach to supersymmetric gauge theories suffers from problems with infrared divergences which greatly complicate multiloop calculations. We eliminate these divergences by introducing a non-local gauge-fixing term. In the background field method this term leads to unusual quantum-background interactions. Functional methods are presented for dealing with these interactions. As an example we compute the two-loop Yang-Mills β-function using the background field method in superspace. We also show how a non-local gauge can be used in ordinary, non-supersymmetric Yang-Mills theory.     

Gravitational Contributions to the Running of Gauge Couplings

Gravitational contributions to the running of gauge couplings arecalculated by using different regularization schemes. As the β function concerns counter-terms of dimension four, only quadratic divergences from the gravitational contributions need to be investigated. A consistent result is obtained by using a symmetry-preserving loop regularization with string-mode regulators which can appropriately treat the quadratic divergences andpreserve non-abelian gauge symmetry. The harmonic gauge conditionfor gravity is used in both diagrammatical and background field calculations, the resulting gravitational corrections to the β function are found to be nonzero, which is different from previous results presented in the existing literatures.     

Soft gauge algebras

Gauge transformations whose algebra closes only modulo field dependent terms (soft gauge algebras) are studied in detail. The results are explicitly applied to a supersymmetric gauge theory, to gravity and to conformal gravity, all seen as gauge theories overx-space; the obvious applications to supergravity are pointed out. A consistency requirement for the gauge transformations of those fields which appear in the algebra is seen to rule out “local translations” as independent gauge transformations.