One-loop Chern-Simons terms in five dimensions

Abstract

We compute one-loop corrections to five-dimensional gauge and gravitational ChernSimons terms induced by integrating out charged massive fields. The considered massive fields are spin-1/2 and spin-3/2 fermions, as well as complex two-forms with first order kinetic terms. Consistency with six-dimensional gravitational anomalies of (1, 0) and (2, 0) theories is shown by interpreting the massive fields as excited Kaluza-Klein modes in a circle compactification. The results are in accordance with the geometric predictions of the M-theory to F-theory duality as well as the comparison with an explicit one-loop computation in heterotic string theory compactified on K3 × S 1 .

Cardy formulae for SUSY theories in d = 4 and d = 6

“…At order r is the curvature two-form on M 5 and A is the dimensional reduction of the G gauge field. The former Chern-Simons term is expected to be fixed by the gravitational anomalies A and B, while the latter is expected to be fixed by the mixed anomaly C. 12 (Note that in 5d, in addition to massive fermions, also massive tensor (two-form) fields generate such Chern-Simons term when they are integrated out [51,52]. This is necessary for the relations below between Chern-Simons terms and anomalies to make sense.)…”

Effective actions in N = 1 $$ \mathcal{N}=1 $$ , D5 supersymmetric gauge theories: harmonic superspace approach

“…In particular, one can argue [14,15] that the 5D Chern-Simons term can be generated by the anomaly terms in the six-dimensional theory. By focusing on a certain class of anomaly-free six-dimensional theories the authors of [14,15] formulated the explicit constraints on the spectrum and supersymmetry content of the six-dimensional theory in terms of the five-dimensional Chern-Simons couplings. Therefore it would be interesting to compute the perturbative quantum corrections in such 5D theories.…”

“…Finally ChernSimons theory can be important in the relation between the 5D SYM and 6D (2, 0) theories. In particular, one can argue [14,15] that the 5D Chern-Simons term can be generated by the anomaly terms in the six-dimensional theory.…”

“…The analytic superfield V ++ turns out to be the single unconstrained potential of the pure 5D, N = 1 SYM theory and all other quantities, associated with this theory, are expressed in its terms. In particular, the other harmonic connection V −− turns out to be uniquely determined in terms of V ++ using the zero-curvature condition 14) where (u…”

“…First of all, in five dimensions the pure U(N ) and SU(N ) Chern-Simons theories have superconformal fixed points [6,7]. Another reason to study the SCS models is that they can be generated by integrating out the massive hypermultiplets in the SYM theory [2,3,14,15] when the hypermultiplets transform in complex representations of the gauge group. For example, if we consider the masses of the hypermultiplets as the UV cut-off, we obtain the Chern-Simons term in the one-loop correction to the classical theory.…”