Self-dual Antisymmetric Tensors Research Articles

One-loop pseudo-Goldstone masses in the minimal SO(10) Higgs model

We calculate the prominent perturbative contributions shaping the one-loop scalar spectrum of the minimal non-supersymmetric renormalizable $SO(10)$ Higgs model whose unified gauge symmetry is spontaneously broken by an adjoint scalar. Focusing on its potentially realistic $45\oplus 126$ variant in which the rank is reduced by a VEV of the 5-index self-dual antisymmetric tensor, we provide a thorough analysis of the corresponding one-loop Coleman-Weinberg potential, paying particular attention to the masses of the potentially tachyonic pseudo-Goldstone bosons (PGBs) transforming as $(8,1,0)$ and $(1,3,0)$ under the Standard Model gauge group. The results confirm the assumed existence of extended regions in the parameter space supporting a locally stable SM-like quantum vacuum inaccessible at the tree-level. The effective potential (EP) tedium is compared to that encountered in the previously studied $45\oplus 16$ $SO(10)$ Higgs model where the polynomial corrections to the relevant pseudo-Goldstone masses turn out to be easily calculable within a very simplified purely diagrammatic approach.

Consistency of the AdS7×S4 reduction and the origin of self-duality in odd dimensions

We discuss the full nonlinear Kaluza–Klein (KK) reduction of the original formulation of d=11 supergravity on AdS7×S4 to gauged maximal (N=4) supergravity in 7 dimensions. We derive the full nonlinear embedding of the d=7 fields in the d=11 fields (“the ansatz”) and check the consistency of the ansatz by deriving the d=7 supersymmetry laws from the d=11 transformation laws in the various sectors. The ansatz itself is nonpolynomial but the final d=7 results are polynomial. The correct d=7 scalar potential is obtained. For most of our results the explicit form of the matrix U connecting the d=7 gravitino to the Killing spinor is not needed, but we derive the equation which U has to satisfy and present the general solution. Requiring that the expressionδF=dδA in d=11 can be written as δd(fields in d=7), we find the ansatz for the 4-form F. It satisfies the Bianchi identities. The corresponding ansatz for the 3-form A modifies the geometrical proposal by Freed et al. by including d=7 scalar fields. A first order formulation for A in d=11 is needed to obtain the d=7 supersymmetry laws and the action for the nonabelian selfdual antisymmetric tensor field Sαβγ,A. Therefore selfduality in odd dimensions originates from a first order formalism in higher dimensions.

Anomalies and inflow on D-branes and O-planes

We derive the general form of the anomaly for chiral spinors and self-dual antisymmetric tensors living on D-brane and O-plane intersections, using both path-integral and index theorem methods. We then show that the anomalous couplings to RR forms of D-branes and O-planes in a general background are precisely those required to cancel these anomalies through the inflow mechanism. This allows, for instance, for local anomaly cancellation in generic orientifold models, the relevant Green-Schwarz term being given by the sum of the anomalous couplings of all the D-branes and O-planes in the model.

Trace anomalies from quantum mechanics

The one-loop anomalies of a d-dimensional quantum field theory can be computed by evaluating the trace of the path integral jacobian matrix J, regulated by an operator exp(−β R ) and taking the limit β to zero. Sometime ago Alvarez-Gaumé and Witten made the observation that one can simplify this evaluation by replacing the operators which appear in J and R by quantum mechanical operators with the same (anti)commutation relations. By rewriting this quantum mechanical trace as a path integral with periodic boundary conditions at time t = 0 and t = β for a one-dimensional supersymmetric nonlinear sigma model, they obtained the chiral anomalies for spin- 1 2 and spin- 3 2 fields and selfdual antisymmetric tensors in d dimensions. One can also apply these ideas to the trace anomalies. Recently a bosonic configuration-space path integral for a particle moving in curved space was proposed by the first author, and the corresponding hamiltonian R was found from the Schrödinger equation. The factors √ g in the path-integral measure were exponentiated by using scalar ghosts, and the trace anomaly for a scalar field in an external gravitational field in d = 2 was obtained. Here we treat the general case of trace anomalies for external gravitational and Yang-Mills fields. We do not introduce a supersymmetric sigma model, but keep the original Dirac matrices γ μ and internal symmetry generators T a in the path integral. As a result, we get a matrix-valued action S. Gauge covariance of the path integral then requires us to define the exponential of the action by time ordering. The computations are simplified by using Riemann normal coordinates. We also replace the scalar ghosts by vector ghosts in order to exhibit the cancellation of all divergences at finite β more clearly. Finally we compute the trace anomalies in d = 2 and d = 4.

Cancellation of gravitational anomalies in d=6 supergravities

The conditions for cancellation of gravitational anomalies in d=6 chiral supergravities based on the systematic use of index theorems are examined here. The authors point out the minimal necessary combinations of chiral fermions (with spin 3/2 and 1/2) and (anti-) self-dual antisymmetric tensors, as well as the corresponding combinations of N=1, d=6 supermultiplets that ensure cancellation of gravitational anomalies.

Gravitational anomalies from the action for self-dual antisymmetric tensor fields in 4k+2 dimensions.

We show that recent actions for a single self-dual antisymmetric tensor field in 4k+2 dimensions lead to the same one-loop gravitational anomalies as obtained a few years ago by Alvarez-Gaum\'e and Witten, who conjectured the necessary Feynman rules in the absence of an action principle.

Gravitational anomalies: Antisymmetric tensor gauge field versus bispinor field

It is shown perturbatively that the gravitational anomaly of the chiral bispinor field is twice as large as that of the self-dual antisymmetric tensor gauge field; in the previous literature they were supposed to agree with each other. This implies that a naive application of Fujikawa's path integral method leads to a wrong result for the anomaly of the self-dual antisymmetric tensor gauge field.

Gravitational Anomaly and Path Integral Jacobian of Anti-Symmetric Tensor Gauge Field

A path integral formula is presented for the covariant gravitational anomaly of the self-dual anti-symmetric tensor gauge field. With the help of this formula, it is shown that the path integral Jacobian of the self-dual field strength under the general coordinate transformation is twice as large as the gravitational anomaly. It is also shown perturbatively that a chiral bi-spinor field accompanied with appropriate Faddeev-Popov ghosts describes a system of two self-dual anti-symmetric tensor gauge fields.

Anomaly-free supergravity theories remain anomaly-free after dimensional reduction

Abstract We show that the anomaly after compactification of a supergravity theory coupled to Yang-Mills matter is usually given by an integral of the original anomaly over the compact space, as long as there are no isometries for the compact space. This means that a supergravity theory, whose anomaly vanishes identically (i.e., without the addition of local counter terms to the action), will remain anomaly-free after compactification to any lower dimension, subject to some restrictions on self-dual antisymmetric tensors. We next consider the case where the original anomaly cancels by the Green-Schwarz mechanism. In this case, again subject to the restrictions on self-dual antisymmetric tensors, the anomaly will still cancel after compactification to any lower dimension D > 2, provided that: (1) There are no U(1) gauge groups after compactification. (2) There exists a three-form field strength H such that d H = (Tr R 0 2 + k Tr F 0 2 ), or that the compact space is chosen such that (Tr R 0 2 + k Tr F 0 2 ) = 0.

Hamiltonian treatment of self-dual antisymmetric tensors

Self-dual antisymmetric tensors occur in certain (4 n + 2)-dimensional supergravity models, in particular the one connected to type IIB superstrings. So far they have been quantized only using light front methods. Here we show that the existing covariant action for such fields leads to a consistent hamiltonian system also for ordinary “timelike” dynamics, although rather complicated second class constraints are present.

Gravitational anomalies

It is shown that in certain parity-violating theories in 4 k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of spin- 1 2 or -3 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.