Small instantons in weakly-gauged holographic models

Small instantons can play an important role in Yang-Mills theories whose gauge couplings are sizeable at small distances. An interesting class of theories where this could occur is in weakly-gauged holographic models (dual to Yang-Mills theories interacting with strongly-coupled CFTs), since gauge couplings are indeed enhanced towards the UV boundary of the 5D AdS space. However, contrary to expectations, we show that small instantons in these non-asymptotically-free models are highly suppressed and ineffective. This is due to the conservation of topological charge that forbids instantons to be localized near the UV boundary. Despite this fact we find non-trivial UV localized instanton-anti-instanton solutions of the Yang-Mills equations where the topological charges annihilate in the AdS bulk. These analytic solutions arise from a 5D conformal transformation of the uplifted 4D instanton. Our analysis therefore reveals unexpected nonperturbative configurations of Yang-Mills theories when they interact with strongly-coupled CFTs.

The NSVZ relations for $$ \mathcal{N} $$ = 1 supersymmetric theories with multiple gauge couplings

We investigate the NSVZ relations for $$ \mathcal{N} $$ N = 1 supersymmetric gauge theories with multiple gauge couplings. As examples, we consider MSSM and the flipped SU(5) model, for which they easily reproduce the results for the two-loop β-functions. For $$ \mathcal{N} $$ N = 1 SQCD interacting with the Abelian gauge superfield we demonstrate that the NSVZ-like equation for the Adler D-function follows from the NSVZ relations. Also we derive all-loop equations describing how the NSVZ equations for theories with multiple gauge couplings change under finite renormalizations. They allow describing a continuous set of NSVZ schemes in which the exact NSVZ β-functions are valid for all gauge coupling constants. Very likely, this class includes the HD+MSL scheme, which is obtained if a theory is regularized by Higher covariant Derivatives and divergences are removed by Minimal Subtractions of Logarithms. That is why we also discuss how one can construct the higher derivative regularization for theories with multiple gauge couplings. Presumably, this regularization allows to derive the NSVZ equations for such theories in all loops. In this paper we make the first step of this derivation, namely, the NSVZ equations for theories with multiple gauge couplings are rewritten in a new form which relates the β-functions to the anomalous dimensions of the quantum gauge superfields, of the Faddeev-Popov ghosts, and of the matter superfields. The equivalence of this new form to the original NSVZ relations follows from the extension of the non-renormalization theorem for the triple gauge-ghost vertices, which is also derived in this paper.

Probing anomalous γγγZ couplings through γZ production in γγ collisions at the CLIC

We have estimated the sensitivity to the anomalous couplings of the γγγZ vertex in the γγ → γZ scattering of the Compton backscattered photons at the CLIC. Both polarized and unpolarized collisions at the e+e− energies 1500 GeV and 3000 GeV are addressed, and anomalous contributions to helicity amplitudes are derived. The differential and total cross sections are calculated. We have obtained 95% C.L. exclusion limits on the anomalous quartic gauge couplings (QGCs). They are compared with corresponding bounds derived for the γγγZ couplings via γZ production at the LHC. The constraints on the anomalous QGCs are one to two orders of magnitude more stringent that at the HL-LHC. The partial-wave unitarity constraints on the anomalous couplings are examined. It is shown that the unitarity is not violated in the region of the anomalous QGCs studied in the paper.

Swampland geometry and the gauge couplings

The purpose of this paper is two-fold. First we review in detail the geometric aspects of the swampland program for supersymmetric 4d effective theories using a new and unifying language we dub “domestic geometry”, the generalization of special Kähler geometry which does not require the underlying manifold to be Kähler or have a complex structure. All 4d SUGRAs are described by domestic geometry. As special Kähler geometries, domestic geometries carry formal brane amplitudes: when the domestic geometry describes the supersymmetric low-energy limit of a consistent quantum theory of gravity, its formal brane amplitudes have the right properties to be actual branes. The main datum of the domestic geometry of a 4d SUGRA is its gauge coupling, seen as a map from a manifold which satisfies the geometric Ooguri-Vafa conjectures to the Siegel variety; to understand the properties of the quantum-consistent gauge couplings we discuss several novel aspects of such “Ooguri-Vafa” manifolds, including their Liouville properties.Our second goal is to present some novel speculation on the extension of the swampland program to non-supersymmetric effective theories of gravity. The idea is that the domestic geometric description of the quantum-consistent effective theories extends, possibly with some qualifications, also to the non-supersymmetric case.

Stability of BPS states and weak coupling limits

We study the stability and spectrum of BPS states in $$ \mathcal{N} $$ N = 2 supergravity. We find evidence, and prove for a large class of cases, that BPS stability exhibits a certain filtration which is partially independent of the value of the gauge couplings. Specifically, for any perturbative value of any gauge coupling g ≪ 1, a BPS state can only decay to some constituents if those constituents do not become infinitely heavier than it in the vanishing coupling limit g → 0. This stability filtration can be mathematically formulated in terms of the monodromy weight filtration of the limiting mixed Hodge structure associated to the vanishing coupling limit. We study various implications of the result for the Swampland program which aims to understand such weak-coupling limits, specifically regarding the nature and presence of an infinite tower of light charged BPS states.

Resummation of terms enhanced by trilinear squark-Higgs couplings in the MSSM

We analyze the appearance of the trilinear squark-Higgs couplings xq in Green functions in the Higgs sector of the MSSM and in threshold corrections to the SM. The results are constraints on maximal powers of xq in QCD-related loop corrections. In practice these often imply all-order resummations of leading or subleading xq contributions in SM-parametrized expressions. We present a variety of all-order resummation relations for ∆λ which include such xq-enhanced terms and different orders in Yukawa and gauge couplings. We contrast which terms cannot be resummed.