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Abstract In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/’t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the γ 5-matrix appearing in gauge interactions is a non-anticommuting object, leading to a breaking of gauge and BRST invariance. Employing an efficient method based on the quantum action principle, we obtain the complete three-loop counterterm action which serves both to render the theory finite and to restore gauge and BRST invariance. The UV singular counterterms involve not only higher order ϵ-poles but also new counterterm structures emerging at the three-loop level for the first time; the finite symmetry-restoring counterterms are restricted to the same structures as at lower loop orders, just with different coefficients, aligning with our expectations. Both the singular and the finite counterterms include structures which cannot be obtained by the standard multiplicative renormalisation. Our results demonstrate that a rigorous treatment of chiral gauge theories with γ 5 defined in the BMHV scheme at the multi-loop level is possible and that the obtained counterterm action is suitable for computer implementations, allowing automated calculations without ambiguities caused by γ 5.

Abstract In recent years, theoretical and phenomenological studies with effective field theories have become a trending and prolific line of research in the field of high-energy physics. In order to discuss present and future prospects concerning automated tools in this field, the SMEFT-Tools 2022 workshop was held at the University of Zurich from 14th–16th September 2022. The current document collects and summarizes the content of this workshop.

Abstract In this work we study type IIB Calabi-Yau orientifold compactifications in the presence of space-time filling D7-branes and O7-planes. In particular, we conclude that α′2 g s -corrections to their DBI actions lead to a modification of the four-dimensional N $$ \mathcal{N} $$ = 1 Kähler potential and coordinates. We focus on the one-modulus case of the geometric background i.e. h 1,1 = 1 where we find that the α′2 g s -correction is of topological nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau orientifold which is wrapped by the D7-branes and O7-plane. This is in agreement with our previous F-theory analysis and provides further evidence for a potential breaking of the no-scale structure at order α′2 g s . Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss α′-corrections from other Dp-branes.

Abstract In this work we analyze F-theory and Type IIB orientifold compactifications to study α′-corrections to the four-dimensional, N $$ \mathcal{N} $$ = 1 effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the G 2 R 3 and (∇G)2 R 2-sector in eleven-dimensions relevant in Calabi-Yau fourfold reductions. We suggest that the three-dimensional, N $$ \mathcal{N} $$ = 2 Kähler coordinates may be expressed as topological integrals depending on the first, second, and third Chern-forms of the divisors of the internal Calabi-Yau fourfold. The divisor integral Ansatz for the Kähler potential and Kähler coordinates may be lifted to four-dimensional, N $$ \mathcal{N} $$ = 1 F-theory vacua. We identify a novel correction to the Kähler potential and coordinates at order α′ 2, which is leading compared to other known corrections in the literature. At weak string coupling the correction arises from the intersection of D7-branes and O7-planes with base divisors and the volume of self-intersection curves of divisors in the base. In the presence of the conjectured novel α′-correction resulting from the divisor interpretation the no-scale structure may be broken. Furthermore, we propose a model independent scenario to achieve non-supersymmetric AdS vacua for Calabi-Yau orientifold backgrounds with negative Euler-characteristic.

Abstract In this note we consider M-theory compactified on a warped Calabi-Yau four-fold including the eight-derivative terms in the eleven-dimensional action known in the literature. We dimensionally reduce this theory on geometries with one Kähler modulus and determine the resulting three-dimensional Kähler potential and complex coordinate. The logarithmic form of the corrections suggests that they might admit a physical interpretation in terms of one-loop corrections to the effective action. Including only the known terms the no-scale condition in three dimensions is broken, but we discuss caveats to this conclusion. In particular, we consider additional new eight-derivative terms in eleven dimensions and show that they are strongly constrained by compatibility with the Calabi-Yau threefold reduction. We examine their impact on the Calabi-Yau fourfold reduction and the restoration of the no-scale property.

Abstract The four- and five-dimensional effective actions of Calabi-Yau threefold compactifications are derived with a focus on terms involving up to four space-time derivatives. The starting points for these reductions are the ten- and eleven-dimensional supergravity actions supplemented with the known eight-derivative corrections that have been inferred from Type II string amplitudes. The corrected background solutions are determined and the fluctuations of the Kähler structure of the compact space and the form-field back-ground are discussed. It is concluded that the two-derivative effective actions for these fluctuations only takes the expected supergravity form if certain additional ten- and eleven-dimensional higher-derivative terms for the form-fields are included. The main results on the four-derivative terms include a detailed treatment of higher-derivative gravity coupled to Kähler structure deformations. This is supplemented by a derivation of the vector sector in reductions to five dimensions. While the general result is only given as an expansion in the fluctuations, a complete treatment of the one-Kähler modulus case is presented for both Type II theories and M-theory.

Abstract We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational α′3-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of O3/O7-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inflation.

We perform a Kaluza–Klein reduction of eleven-dimensional supergravity on a Calabi–Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional two-derivative N=2 effective action. We focus on the effective Einstein–Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kähler potential and complex coordinates. The classical expressions for the Kähler coordinates are non-trivially modified by terms containing the third Chern form of the background Calabi–Yau fourfold, while the functional form of the Kähler potential is shown to be uncorrected. We omit terms proportional to the non-harmonic part of the third Chern form. For elliptically fibered Calabi–Yau fourfolds the corrections can be uplifted to a four-dimensional F-theory compactification. We argue that also the four-dimensional N=1 Kähler coordinates receive non-trivial corrections. We find a simple expression for the induced corrections for different Abelian and non-Abelian seven-brane configurations by scanning over many Calabi–Yau fourfolds with resolved singularities. The interpretation of this expression leads us to conjecture that the higher-curvature corrections correspond to α′2 corrections that arise from open strings at the self-intersection of seven-branes.