Abstract
Abstract We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons 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.
Highlights
The derivation of a Wilsonian low-energy effective action amounts to integrating out all excitations beyond a chosen cutoff mass scale and obtaining a theory with modified couplings for the remaining degrees of freedom
We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons terms induced by integrating out charged massive fields
In this paper we have studied Chern-Simons terms in five-dimensional gauge theories with non-Abelian gauge groups
Summary
The derivation of a Wilsonian low-energy effective action amounts to integrating out all excitations beyond a chosen cutoff mass scale and obtaining a theory with modified couplings for the remaining degrees of freedom. Four-dimensional examples are furnished by Goldstone-Wilczek currents [3] and Wess-Zumino terms [4] generated by integrating out a fermion that becomes massive via Yukawa coupling to a scalar that gets a non-vanishing VEV They are independent of the fermion mass and have to be included in the low-energy effective action even in the limit in which it is taken to infinity. The kinetic and mass terms of the fermions are of standard form while the complex two-forms admit first order kinetic terms The latter feature is possible in odd-dimensional theories and is crucial for the fields to introduce corrections to Chern-Simons couplings. The summation over the various massive modes propagating through the loop in the field theory picture corresponds to integrating over the moduli space of world-sheet tori from the string perspective that captures the contribution of all CFT excitations. In appendix D we perform the calculation of a torus integral that appears in the string theory computation
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