Using Covariant Polarisation Sums in QCD

Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

Fermion and gluon spectral functions far from equilibrium

Motivated by the quark-gluon plasma, we develop a simulation method to obtain the spectral function of (Wilson) fermions non-perturbatively in a non-Abelian gauge theory with large gluon occupation numbers [1]. We apply our method to a non-Abelian plasma close to its non-thermal fixed point, i.e., in a far-from-equilibrium self-similar regime, and find mostly very good agreement with perturbative hard loop (HTL) calculations. For the first time, we extract the full momentum dependence of the damping rate of fermionic collective excitations and compare our results to recent non-perturbative extractions of gluonic spectral functions in two and three spatial dimensions [2, 3].

Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit of interest introduces a scale hierarchy in the problem, asymptotics of the partition function is obtained in the Wilsonian approach by i) decomposing (in some suitable scheme) the BPS moduli space into various patches according to the set of light fields (lighter than the scheme dependent cut-off Λ) they support, ii) localizing the partition function of the effective field theory on each patch (with cut-offs set by the scheme), and iii) summing up the contributions of all patches to obtain the final asymptotic result (which is scheme-independent and accurate as Λ → ∞). Our prototype concerns the Cardy-like asymptotics of the 4d superconformal index, which has been of interest recently for its application to black hole microstate counting in AdS5/CFT4. As a byproduct of our analysis we obtain the most general asymptotic expression for the index of gauge theories in the Cardy-like limit, encompassing and extending all previous results.

Decomposition of the static potential in the Maximal Abelian gauge

Decomposition of SU(2) gauge field into monopole and monopoleless components is studied in SU(2) gluodynamics and in QC2D with zero and nonzero quark chemical potential after fixing MA gauge. For both components we calculate respective static potential and compare their sum with the nonabelian static potential. We demonstrate good agreement in the confinement phase and discuss the implications of our results.

Gravitational wave trispectrum in the axion-SU(2) model

We study the trispectrum of the gravitational waves (GWs) generated through the dynamics of an axionic spectator field and SU(2) gauge fields during inflation. In non-Abelian gauge theory, the gauge fields have four-point self-interactions, which induce the tree-level GW trispectrum. We formulate this type of the GW trispectrum including the non-dynamical contributions and evaluate it in the equilateral limit as a unique signal of this model. We find that the ratio of the GW trispectrum to the cube of the scalar power spectrum can be as large as 𝒪(106) in the viable parameter space, which could be captured in the CMB observations.

Dark QCD matters

We investigate the nightmare scenario of dark sectors that are made of non-abelian gauge theories with fermions, gravitationally coupled to the Standard Model (SM). While testing these scenarios is experimentally challenging, they are strongly motivated by the accidental stability of dark baryons and pions, that explain the cosmological stability of dark matter (DM). We study the production of these sectors which are minimally populated through gravitational freeze-in, leading to a dark sector temperature much lower than the SM, or through inflaton decay, or renormalizable interactions producing warmer DM. Despite having only gravitational couplings with the SM these scenarios turn out to be rather predictive depending roughly on three parameters: the dark sector temperature, the confinement scale and the dark pion mass. In particular, when the initial temperature is comparable to the SM one these scenarios are very constrained by structure formation, ∆Neff and limits on DM self-interactions. Dark sectors with same temperature or warmer than SM are typically excluded.

One-loop matrix elements of effective superstring interactions: α′-expanding loop integrands

In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D2kFn and D2kRn in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α′. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α′. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

Dark photon bounds in the dark EFT

Dark photons are massive abelian gauge bosons that interact with ordinary photons via a kinetic mixing with the hypercharge field strength tensor. This theory is probed by a variety of different experiments and limits are set on a combination of the dark photon mass and kinetic mixing parameter. These limits can however be strongly modified by the presence of additional heavy degrees of freedom. Using the framework of dark effective field theory, we study how robust are the current experimental bounds when these new states are present. We focus in particular on the possible existence of a dark dipole interaction between the Standard Model leptons and the dark photon. We show that, under certain assumptions, the presence of a dark dipole modifies existing supernovæ bounds for cut-off scales up to $$ \mathcal{O} $$ O (10–100 TeV). On the other hand, terrestrial experiments, such as LSND and E137, can probe cut-off scales up to $$ \mathcal{O} $$ O (3 TeV). For the latter experiment we highlight that the bound may extend down to vanishing kinetic mixing.

Anomaly-free Abelian gauge symmetries with Dirac seesaws

We perform a systematic analysis of Standard Model extensions with an additional anomaly-free gauge U(1) symmetry, to generate tree-level Dirac neutrino masses. An anomaly-free symmetry demands nontrivial conditions on the charges of the unavoidable new states. An intensive scan was performed, looking for solutions generating neutrino masses by the type-I and type-II tree-level Dirac seesaw mechanism, via operators with dimension 5 and 6, that correspond to active or dark symmetries. Special attention was paid to the cases featuring no extra massless chiral fermions or multicomponent dark matter with unconditional stability.

The colored Jones polynomials as vortex partition functions

We construct 3D $$ \mathcal{N} $$ N = 2 abelian gauge theories on $$ \mathbbm{S} $$ S 2 × $$ \mathbbm{S} $$ S 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones polynomials of knots in $$ \mathbbm{S} $$ S 3. The colored Jones polynomials are obtained as the Wilson loop expectation values along knots in SU(2) Chern-Simons gauge theories on $$ \mathbbm{S} $$ S 3, and then our construction provides an explicit correspondence between 3D $$ \mathcal{N} $$ N = 2 abelian gauge theories and 3D SU(2) Chern-Simons gauge theories. We verify, in particular, the applicability of our constructions to a class of tangle diagrams of 2-bridge knots with certain specific twists.