Space-time geometry and symmetry breaking

We look for solutions of the Einstein-Yang-Mills equations in a 4 + D dimensional space-time. We find solutions where the first 4 dimensions are a flat Minkowskian space-time, while the D others are a compact, space-like manifold of small size. Such solutions can be obtained for an arbitrary compact gauge group K and are invariant under a sub-group G of K related to the space-time geometry. This shows that 4 + D dimensional gravity can give a mechanism for the super-strong symmetry breaking needed in grand unified field theories without introducing Higgs scalars.     

Sphalerons on orbifolds

In this work, we study the electroweak sphalerons in a 5D background, where the fifth dimension lies on an interval. We consider two specific cases: flat space-time and the anti-de Sitter space-time compactified on S ¹/Z ₂. In our work, we take the SU(2) gauge–Higgs model, where the gauge fields reside in the 5D bulk; but the Higgs doublet is confined in one brane. We find that the results in this model are close to those of the 4D Standard Model (SM). The existence of the warp effect, as well as the heaviness of the gauge Kaluza–Klein modes make the results extremely close to the SM ones.     

Exact calculation of the Fermion determinant in chiral QCD2 reflecting the full regularization dependence

The fermion determinant of non-abelian anomalous gauge theory in two space-time dimensions is computed using the path-integral approach. The regularization dependence of the fermion determinant is worked out. Apart from a regularization dependentA ² term, the fermion determinant contains a Wess-Zumino-Witten anomaly functional.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

The trace anomaly in coloured black holes

The influence of the trace anomaly of the energy-momentum tensor of gauge theories is discussed in a spherically symmetric space-time. It is found that for pure electric and magnetic fields, the point β(g) = ?g represents a phase transition from any asymptotically flat metric to an asymptotically non-flat metric which turns out to be confining in the electric case.     

Anomalies and gauge symmetry

Anomalies are known to have an intrinsic geometrical meaning. Using a formalism where the gauge condition is never made explicit we reanalyze the gauge theory anomaly problem. By requiring simultaneously the BRS and anti-BRS invariances, we do not need to use in our study the gauge dependent anti-ghost equation of motion. Then all equations definining the anomaly are independent of all parameters specifying the lagrangian. Not only does this stress explicitly the geometrical nature of the anomaly problem, but it allows for a single analysis for all possible BRS and anti-BRS invariant gauges, including those with four-ghost interactions. Our method for solving the anomaly equations is as a new sign of the relevance of the formalism in which the ghost components are unified with those of the classical gauge field, the ghost fields playing the role of a “connection” along unphysical directions. We recover the ABJ anomaly directly from the structure of BRS equations, as a straightforward application of the Chern-Weil theorem in some enlarged space. The method can be formally extended to higher space-time dimensions, and a general formula for “anomalies” in any even dimension is given.     

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.     

Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.     

Chiral U(1) anomaly in D=4 super Yang-Mills theory coupled to supergravity

We evaluate the chiral U(1) anomaly in D=4 supersymmetric Yang-Mills theory coupled to supergravity. We consider not only the minimal coupling between the gauge fields and fermions but also the interaction term which mixes the gravitino and the gaugino. We show that the mixing interaction gives new contributions to the anomaly.     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Unified geometry of antisymmetric tensor gauge fields and gravity

Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ω_r?1M,U(1)), the U(1) bundles over the space of all (r?1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω₁M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.     

Superstring theory

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(n) or Sp(2n) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D = 10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N = 4, D = 4 super Yang-Mills theory and SST II reduces to N = 8, D = 4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions.     

Gravitational anomalies

The effective action for fermions moving in external gravitational and gauge fields is analyzed in terms of the corresponding external field propagator. The central object in our approach is the covariant energy-momentum tensor which is extracted from the regular part of the propagator at short distances. It is shown that the Lorentz anomaly, the conformal anomaly and the gauge anomaly can be expressed in terms of the local polynomials which determine the singular part of the propagator. (There are no coordinate anomalies.) Except for the conformal anomaly, for which we give explicit representations only ind<=4, we consider an arbitrary number of dimensions.     

Radiative decay of mesons and anomaly in 2+1 dimensions

In 2+1 space-time, we study the radiative decay of mesons with Yukawa couplings to two and four component fermions. In a four component theory, the electromagnetic current is free of parity odd radiative corrections; however an axialU(1) current is shown to develop a finite vacuum expectation value. Unlike even dimensions this anomaly is temperature dependent and does not play any role in the radiative decay. We calculate the effective action for the mesons and show that a finite kinetic term for these fields is induced at the one-loop level and vanishes as the temperature goes to infinity.     

Elliptic index and superstring effective actions

Certain N = 1 supersymmetric string one-loop effective actions can be obtained directly from the path integral. As the computation is essentially the same as the one leading to the index of the Dirac-Ramond operator, they are determined by the gauge and gravitational anomaly structure of the theory. Specifically, we calculate the four-point effective action in ten dimensions, the corrections to the kinetic terms in d = 6 (including auxiliary fields) and the Fayet-Iliopoulos D-term in d = 4. We also compute the β-function of four-dimensional N = 2 theories from the elliptic genus in d = 6. Furthermore, we derive supersymmetry Ward type identities in terms of Kac-Moody characters, relating parity conserving with parity violating amplitudes.     

Ramond-Neveu-Schwarz string with new boundary conditions

For the Ramond-Neveu-Schwarz string in D space-time dimensions we seek boundary conditions which preserve Poincaré invariance in d dimensions, d<D. We obtain twisted closed and twisted open strings preserving Gervais-Sakita supersymmetry. Covariant BRST quantization yields D=10. For some boundary conditions, partition functions exhibit space-time supersymmetry.     

Anomalies in gravity-coupled SU(N) Yang-Mills theory

In a general even space-time dimension I consider spin-1/2 fermions coupled to SU(N) Yang-Mills fields and to gravity. It is shown (unexpectedly) that, once the chiral gauge anomaly is cancelled, gravitational anomalies do not further constrain the fermion representation.     

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D₀ for different values of dimensions including the most important practical cases D₀ = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added.     

Strings in the harmonic gauge

The bosonic string is quantized in a path-integral formulation in harmonic gauge. The BRST transformations are identified and the stress tensor is constructed. The conformal anomaly is computed, and has the standard (D−26) form. The ghost number current is shown to have no anomalies, even on a curved world sheet.