Anomaly Cancellation Mechanism Research Articles

String unification, universal one-loop corrections and strongly coupled heterotic string theory

We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string — M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of the threshold corrections to the anomaly cancellation mechanism.

“Anomalous” U( l) symmetry in orbifold string models

“Anomalous” U(1) gauge symmetry with a Green-Schwarz anomaly cancellation mechanism is discussed in the orbifold construction of four-dimensional heterotic string models. Some conditions are given as criteria to have “anomalous” U(1) in orbifold string models. In particular, “anomalous” U(1) is absent if the massless twisted matter has no mixing between visible and hidden sectors or if a certain type of discrete symmetries are found. We then give a general procedure for classifying orbifold models with “anomalous” U(1) and for identifying the “anomalous” U(1) basis. We illustrate our procedure in Z 3 and Z 4 orbifold models. According to our procedure, the classification of “anomalous” U(1) can be reduced to classification in the absence of a Wilson line. We also discuss discrete symmetries left unbroken after the “anomalous” U(1) breaking. This includes a possible relation between “anomalous” U(1) and discrete R symmetries.

The supersymmetric version of the Green-Schwarz anomaly cancellation mechanism

The N = 1, D = 10 Supergravity-Super-Yang-Mills (SUGRA-SYM) theory is plagued by ABBJ gauge and Lorentz anomalies which are cancelled via the Green-Schwarz anomaly cancellation mechanism. Due to the fact that the ABBJ anomalies are not invariant under supersymmetry (SUSY) transformations one concludes that the theory is plagued also by a SUSY anomaly. For the gauge groups SO(32) and E 8 × E 8 we compute this SUSY anomaly, by solving a coupled cohomology problem, and we show that it can be cancelled by subtracting from the action the known Green-Schwarz counterterm, the same which cancels also the ABBJ anomaly, the expected result. Finally, we argue that the corresponding mechanism does not apply in the dual SUGRA-SYM, related to the heterotic five-brane.

All-loop gauge couplings from anomaly cancellation in string effective theories

We derive, to all orders in perturbation theory, the E 8 gauge coupling and the modified dilaton-axion Kähler potential for the effective theories of a class of d = 4, N = 1 heterotic string models. The derivation relies on an extended version of the Green-Schwarz anomaly cancellation mechanism, and exploits target-space duality invariance. Although we deal with field-dependent effective gauge couplings and scales in a non-renormalizable supergravity theory, we derive for them a renormalization group equation as a relation among dynamical fields. When expectation values of these fields are considered, our results agree with those previously obtained in renormalizable theories with N = 1 global supersymmetry. We finally comment on possible generalizations of the present results.

Generalized Green-Schwarz anomaly cancellation mechanism.

We show that the chiral anomaly can be canceled by a single antisymmetric tensor if the anomaly form factorizes into the product of two invariant polynomials of curvature two-forms, R and F. This generalizes the Green-Schwarz cancellation mechanism, where the factorization is of the form (Tr${R}^{2}$-Tr${F}^{2}$) times an invariant polynomial. The Yang-Mills group constraints differ from those obtained by the Green-Schwarz mechanism if the anomaly form is factorized differently and thus new anomaly-free theories emerge. This generalized mechanism works for any theories in D=4k dimensions and nonsupergravity theories in D=4k-2. However, for supergravity-type theories in D=4k-2 only the original Green-Schwarz factorization works. We explicitly construct many anomaly-free theories in D=8 and D=10, using the generalized mechanism.

4D supergravity coupled to an antisymmetric tensor field with Green-Schwarz mechanism

We derive the component lagrangian for general matter coupling to 4D supergravity of a real linear multiplet, containing an antisymmetric tensor field, which transforms nontrivially under gauge and Lorentz transformations, as it comes from the Green-Schwarz anomaly cancellation mechanism in D = 10. It is found that local supersymmetry requires a third Chern-Simons form related to the axial gauge field of conformal supergravity.

Massive vector multiplets from superstrings

The four-dimensional Green-Schwarz anomaly cancellation mechanism with a surviving U(1) gauge group is described in the context of standard tensor calculus (superspace) techniques for local supersymmetry. This phenomenon is “dual” to the case in which a massless vector field is eaten up by an antisymmetric tensor which thereby describes a massive spin-one field. Both mechanisms are motivated by recent string-loop calculations. Unlike the case of some supergravity models, these mechanisms seem unable (order by order, at least) to break supersymmetry while keeping the cosmological constant vanishing.

The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms

A mechanism is exhibited which ensures that N=1, D=4 new minimal supergravity is free of Lorentz×U(1) anomalies, for any coupling to matter, although it contains an abelian chiral gauge field. This is achieved through the determination of a new supergravity algebra characterized by the presence of a U(1)×Lorentz Chern-Simon form in the field strength of a two-form gauge field. Our analysis provides therefore an example in which Chern-Simon type interactions do occur, while preserving local supersymmetry.

Incorporation ofCPviolation with a unified renormalizable gauge theory

A unified renormalizable gauge theory with $\mathrm{CP}$ violation is presented without having to introduce heavy leptons. The theory utilizes three triples of quarks and three charmed quarks. Models in the SU(2) \ifmmode\times\else\texttimes\fi{} U(1) and SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) \ifmmode\times\else\texttimes\fi{} U(1) gauge groups are constructed. The $\mathrm{CP}$-violating phases are in the hadronic sector which is partly composed of a mixture of two triples. The lepton-hadron anomaly cancellation mechanism is adopted, and a superweak type of $\mathrm{CP}$ violation results from the model.