Coleman-Weinberg symmetry breaking in the chiral SU(n) × SU(n) linear σ model

The onset of symmetry breaking in the chiral SU(n) × SU(n) linear σ model is investigated. It is shown that the model possesses no stable fixed points in d = 4 ? ? dimensions and that the chiral symmetry of the theory can be broken via the CW mechanism when d = 4. The implications of these results are discussed.     

Cohomological extension of Spin(7)-invariant super-Yang–Mills theory in eight dimensions

It is shown that the Spin(7)-invariant super-Yang–Mills theory in eight dimensions, which relies on the existence of the Cayley invariant, permits the construction of a cohomological extension, which relies on the existence of the eight-dimensional analogue of the Pontryagin invariant arising from a quartic chiral primary operator.     

Modular invariance,chiral anomalies and contact terms

The chiral anomaly in heterotic strings with full and partial modular invariance in D = 2n + 2 dimensions is calculated. The boundary terms which were present in previous calculations are shown to be cancelled in the modular-invariant case by contact terms, which can be obtained by an appropriate analytic continuation. The relation to the low-energy field theory is explained. In theories with partial modular invariance, an expression for the anomaly iis obtained and shown to be non-zero in general.     

Spontaneous breaking of supersymmetry through dimensional reduction

A general technique for deriving consistent theories with spontaneously broken supersymmetry and massive gravitinos is illustrated by exploiting the chiral invariance of N = 1 supergravity in four dimensions to construct a theory with broken N = 2 supersymmetry in three dimensions.     

Finiteness of the chiral anomaly graph in higher dimensions

The chiral anomaly graph in 2n dimensions is shown to be completely finite, independent of any constraints which would be imposed from vector-current conservation or Bose-symmetry. There is an n-fold ambiguity present in the graph which guarantees that all current divergences are equivalent in all (self-consistent) perturbative regulating procedures. The chiral anomaly is shown to reside in the alternating sum of current divergences. The ambiguity structure of the chiral anomaly graph in the Pauli-Villars scheme is explicitly computed as a specific example of this general result.     

The gauge field as chiral field on the path and its integrability

It is shown that the gauge theory is equivalent to the chiral theory on the path. As a consequence the results obtained for chiral theory inD-space-time dimension may be carried over for gauge fields inD+1 dimensions. In particular, this leads to the integrability of the classical 3-dimensional Yang-Mills theory in terms of the path variables.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Chiral symmetry and functional integral

The change in the fermionic functional integral measure under chiral rotations is analyzed. Using the ζ-function method, the evaluation of chiral Jacobians to theories including nonhermitian Dirac operators D, can be extended in a natural way. (This being of interest, for example, in connection with the Weinberg-Salam model or with the relativistic string theory.) Results are compared with those obtained following other approaches, the possible discrepancies are analyzed and the equivalence of the different methods under certain conditions on D is proved. Also shown is how to compute the Jacobian for the case of a finite chiral transformation and this result is used to develop a sort of path-integral version of bosonization in d = 2 space-time dimensions. This result is used to solve in a very simple and economical way relevant d = 2 fermionic models. Furthermore, some interesting features in connection with the θ-vacuum in d = 2,4 gauge theories are discussed.     

Complex Chiral Bosons and Their Weyl Fermionic Representation

The complex chiral boson model is proposed. We quantize the theory by using Dirac algorithm and discuss the BRST aspects of the complex chiral boson theory. It is also shown that at the quantum level the theory can be expressed in terms of a Weyl fermionic representation. This suggests that the chiral bosons and Weyl fermions in two dimensions be equivalent in their dual form.     

Lorentz anomaly in arbitrary dimensions

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelian gauge fields do in even dimensions larger than or equal to six. The anomaly is proportional toD/2–1 power to the charge, whereD is a number of space-time dimensions.     

Covariant quantization of chiral bosons and anomaly cancellation

A bosonic string with D spacetime dimensions, R right-moving internal scalars and L left-moving ones can be quantized canonically and is free from local anomaliesif R=L=26−D. Actions for such string theories can be written using Siegel's action for chiral bosons, but anomaly cancellation requires D=0, R=L=26. An action is presented that describes chiral string theories provided R=L=26−D and the physical spectrum is shown to be identical to that of the canonically constructed theory. Supersymmetry, curved backgrounds and global anomalies are briefly discussed.     

The heterotic string is a soliton

It is shown that the Type IIA superstring compactified on K3 has a smooth string soliton with the same zero mode structure as the heterotic string compactified on a four-torus, thus providing new evidence for a conjectured exact duality between the two six-dimensional string theories. The chiral worldsheet bosons arise as zero modes of Ramond-Ramond fields of the IIA string theory and live on a signature (20,4) even, self-dual lattice. Stable, finite loops of soliton string provide the charged Ramond-Ramond states necessary for enhanced gauge symmetries at degeneration points of the K3 surface. It is also shown that Type IIB strings toroidally compactified to six dimensions have a multiplet of string solutions with Type II worldsheets.     

Supersymmetric gauge anomalies in 2 and 4 dimensions from generalized descent-equations

Via a supersymmetric generalization of the descent-equations we derive in Wess-Zumino gauge explicit expressions for chiral anomalies inN=1 supersymmetric Yang-Mills theory for space-time dimensions 2 and 4.     

The weak-coupling phase of lattice spin and gauge models

We analyze the lattice weak-coupling (w.c.) expansion of O(N), CP^N?1 and chiral spin models, and of large-N reduced chiral and gauge models.We find that the w.c. expansion always agrees with mean field results, whenever comparable, for arbitrary space-time dimensions, and that the expansion of the reduced models agrees with that of the original ones. However, w.c. results disagree with one-dimensional large-N and (old and new) exact results. We explain this phenomenon as a failure of the analytic continuation from higher dimensions that defines lattice w.c. perturbation theory for massless models (even if infrared singularities always cancel).We use an improved version of the mean field (m.f.) technique suitable for reduced models. We compute the m.f. approximation of chiral models and use this result to determine the large-d (m.f.) behaviour of reduced gauge models, finding agreement with standard Wilson theory results.We give a new characterization of large-N chiral models in terms of the single-link integral for the adjoint representation of SU(N).     

Saddle-points in the twisted reduced chiral model

It is shown that the abnormal behaviour found in numerical simulations of twisted reduced SU(N→∞) chiral model in two dimensions results from fluctuations around a non-trivial extremum of the action. The possible rôle of such saddle-points in the crossover to the strong coupling regime is discussed.     

Gauged N = 8 supergravity in five dimensions

We construct gauged N = 8 supergravity theories in five dimensions. Instead of the twenty-seven vector fields of the ungauged theory, the gauged theories contain fifteen vector fields and twelve second-rank antisymmetric tensor fields satisfying self-dual field equations. The fifteen vector fields can be used to gauge any of the fifteen-dimensional semisimple subgroups of SL(6,R), specially SO(p, 6?p) for p = 0, 1, 2, 3. The gauged theories also have a physical global SU(1,1) symmetry which survives from the E₆₍₆₎ symmetry of the ungauged theory. This SU(1,1) for the SO(6) gauging is presumably related to that of the chiral N = 2 theory in ten dimensions. In our formalism we maintain a composite local USp(8) symmetry analogous to SU(8) in four dimensions.     

The fate of the U(1) goldstone boson

In the framework of a manifestly covariant formulation of (non-Abelian) gauge theories, we analyse what the gauge invariance (BRS invariance) implies for the problem of the Goldstone boson associated with the conserved U(1) axial vector current. Based on the symmetry consideration of gauge invariance only, it is shown that the Goldstone boson does not appear as a physical particle at all, if and only if the Faddeev-Popov (FP) ghost forms a massless bound state with the gauge boson in a pseudoscalar channel. This decoupling of the Goldstone boson from the physical sector is not caused by the Goldstone dipole proposed by Kogut and Susskind, but by a Goldstone quartet including the FP ghost bound state. This decoupling mechanism by the Goldstone quartet can be shown to become equivalent to that of the Goldstone dipole, only in a special case, i.e., the Schwinger model which is an Abelian theory in two dimensions. In the Abelian gauge theory in four dimensions, the chiral U(1) Goldstone boson necessarily appears as a physical particle.     

Quantization of chiral gauge theories in two-dimensions

It is shown that both abelian and non abelian chiral gauge theories in two dimensions can be made gauge invariant at the quantum level by adding a scalar field. In the bosonized form of the theory, the scalar field appears in a gauged Wess-Zumino action. The current algebra of the extended abelian theory is shown to be free of anomalous terms.     

The Wess-Zumino term in lattice theories

The chiral property of the Wilson lattice fermion is investigated. A chiral-invariant four-Fermi model, in which chiral symmetry is dynamically broken, is considered in 2 and 4 dimensions. The Wess-Zumino term is calculated in the 1/N_c expansion. In 2 dimensions, the Wess-Zumino term appears from the Wilson term in the desired form. However, in 4 dimensions the mass-independent one does not appear. The physical reason for this result is discussed.