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Abstract We calculate the chiral effective superpotential in 4D𝓝=1, SU(N) super Yang-Mills theory coupled to chiral matter in one- and two-loop approximations. It is found that the one-loop contribution to the chiral effective potential is always finite and is expressed in terms of a specific triangle integral. The two-loop contributions generated by purely chiral vertices turned out to be finite as well. The chiral effective potential stipulated by supergraphs with gauge superfield subgraphs is finite for the supergraphs with no divergent subgraphs. In the case of the finite𝓝=2SYM theory, the two-loop chiral contributions to the effective action are significanlty simplified. The leading large N behavior of the chiral effective superpotential in finite𝓝=2super-Yang-Mills models with SU(N) gauge symmetry is studied and it is shown that the exact form in the coupling constant of the chiral effective superpotential can be found.

Abstract Through the calculation of the matrix element of the singlet axial-current operator between the vacuum and a pair of gluons in dimensional regularization with an anti-commuting γ 5 defined in a Kreimer-scheme variant, we find that additional renormalization counter-terms proportional to the Chern-Simons current operator are needed starting from O 𝓞 ( α s 2 α_(s)² ) in QCD. This is in contrast to the well-known purely multiplicative renormalization of the singlet axial-current operator defined with a non-anticommuting γ 5. Consequently, without introducing compensation terms in the form of additional renormalization, the Adler-Bell-Jackiw anomaly equation does not hold automatically in the bare form in this kind of schemes. We determine the corresponding (gauge-dependent) coefficient to O 𝓞 ( α s 3 α_(s)³ ) in QCD, using a variant of the original Kreimer prescription which is implemented in our computation in terms of the standard cyclic trace together with a constructively-defined γ 5. Owing to the factorized form of these divergences, intimately related to the axial anomaly, we further performed a check, using concrete examples, that with γ 5 treated in this way, the axial-current operator needs no more additional renormalization in dimensional regularization but only for non-anomalous amplitudes in a perturbatively renormalizable theory. To be complete, we provide a few additional ingredients needed for a proposed extension of the algorithmic procedure formulated in the above analysis to potential applications to a renormalizable anomaly-free chiral gauge theory, i.e. the electroweak theory.

A bstract We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the G N → 0 limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II 1 , implying the existence of an entropy maximizing state, which realizes a version of Jacobson’s entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose modular flow is geometric at an instant in time. Our results generalize the recent work of Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the static patch of de Sitter space.

We derive the third subleading ((NLO)-L-3) corrections of the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (PN) gravity. These corrections consist of contributions from 4 sectors for generic compact binaries, that enter at the fifth PN order. One of these contributions is due to a new tidal interaction, that is unique to the sectors with spin, and complements the first tidal interaction that also enters at this PN order in the simple point-mass sector. The evaluation of Feynman graphs is carried out in a generic dimension via advanced multi-loop methods, and gives rise to dimensional-regularization poles in conjunction with logarithms. At these higher-spin sectors the reduction of generalized Lagrangians entails redefinitions of the position beyond linear order. We provide here the most general Lagrangians and Hamiltonians. We then specify the latter to simplified configurations, and derive the consequent gauge-invariant relations among the binding energy, angular momentum, and frequency. We end with a derivation of all the scattering angles that correspond to an extension of our Hamiltonians to the scattering problem in the simplified aligned-spins configuration, as a guide to scattering-amplitudes studies.

A bstract Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

Abstract We explore the relation between two distinct prescriptions for γ 5 in dimensional regularization — the Breitenlohner Maison t’Hooft Veltman (BMHV) scheme and Naive Dimensional Regularisation (NDR). The BMHV scheme is the only algebraically consistent scheme, but necessitates chiral symmetry restoring counterterms and it is computationally more expensive, limiting its practical use. We show how the quantum effective action can be translated between both schemes and present these translation rules for the Wilson Coefficients of the Standard Model Effective Field Theory (SMEFT), that can easily be implemented into automated tools for SMEFT computations. Finally, we examine how this scheme dependence manifests itself in matching calculations, identifying the cases in which the dependence cancels in the final result. To examplify this, we consider a concrete UV scenario matched onto the SMEFT at one-loop order in both schemes. Our work aims to facilitate more accurate SMEFT computations and can be considered as a first step towards a comprehensive map between the two continuation schemes.

A bstract The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the ’t Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and γ 5 in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the ’t Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in D dimensions. Our results can be applied in next-to-leading-log calculations in the ’t Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

A bstract A general analysis of line defect renormalisation group (RG) flows in the ε expansion below d = 4 dimensions is undertaken. The defect beta function for general scalar-fermion bulk theories is computed to next-to-leading order in the bulk couplings. Scalar models as well as scalar-fermion models with various global symmetries in the bulk are considered at leading non-trivial order. Different types of potential infrared (IR) defect conformal field theories (dCFTs) and their RG stability are discussed. The possibility of multiple IR stable dCFTs is realised in specific examples with hypertetrahedral symmetry in the bulk. The one-point function coefficient of the order parameter in the stable IR dCFT of the cubic model is computed at next-to-leading order and compared with that in the IR dCFT of the Heisenberg model.

A bstract We present the first part of a systematic calculation of the two-loop anomalous dimensions in the low-energy effective field theory (LEFT): the effects at dimension five in the power counting. Our calculation is performed in a basis with generic mass matrices. We employ the algebraically consistent ’t Hooft-Veltman scheme for γ 5 and we correct for evanescent as well as chiral-symmetry-breaking effects by including the appropriate finite counterterms. We also provide results for the CP -even sector in a scheme that coincides with naive dimensional regularization. We discuss two methods to avoid the explicit construction of gauge-variant operators, which in principle are needed for the cancellation of sub-divergences, even in the background-field method. The two methods are consistent with each other and with existing partial results. Our work is a further step towards a complete EFT framework for physics beyond the Standard Model at next-to-leading-logarithmic accuracy.

A bstract Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats and subtleties that got lost in recent discussions, and spelling out others that to our best knowledge have not been studied in detail. We discuss the consequences of these concepts for the properties of the graviton propagator. Finally, we provide examples of propagators satisfying unitarity and causality, while avoiding tachyonic and vacuum instabilities, and allowing for an analytic Wick rotation.