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Abstract Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm c T derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.

Abstract We present a systematic method for the derivation of a relation which connects the correlation function of operators on the straight Maldacena-Wilson line with the integrability data for the cusp anomalous dimension. As we show, the derivation requires very careful treatment of the UV divergences. Our method opens a way to derive infinitely many constraints on integrals of multi-point correlation functions, relating them with the integrability data for the generalised cusp anomalous dimension governed by the Quantum Spectral Curve. Such constraints have been shown recently to be very powerful in combination with the numerical conformal bootstrap, leading to very narrow non-perturbative bounds on conformal data beyond the spectrum.

Abstract We study the γ-deformation of the planar N $$ \mathcal{N} $$ = 4 super Yang-Mills theory which breaks all supersymmetries but is expected to preserve integrability of the model. We focus on the operator Tr (ϕ 1 ϕ 1) built from two scalars, whose integrability description has been questioned before due to contributions from double-trace counterterms. We show that despite these subtle effects, the integrability-based Quantum Spectral Curve (QSC) framework works perfectly for this state and in particular reproduces the known 1-loop prediction. This resolves an earlier controversy concerning this operator and provides further evidence that the γ-deformed model is an integrable CFT at least in the planar limit. We use the QSC to compute the first 5 weak coupling orders of the anomalous dimension analytically, matching known results in the fishnet limit, and also compute it numerically all the way from weak to strong coupling. We also utilize this data to extract a new coefficient of the beta function of the double-trace operator couplings.

Abstract We continue to develop Bootstrability — a method merging Integrability and Conformal Bootstrap to extract CFT data in integrable conformal gauge theories such as N $$ \mathcal{N} $$ = 4 SYM. In this paper, we consider the 1D defect CFT defined on a 1 2 $$ \frac{1}{2} $$ -BPS Wilson line in the theory, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions — known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constant of the first non-protected state, giving this observable with seven digits precision for the ’t Hooft coupling in the intermediate coupling region λ 4 π ~ 1 $$ \frac{\sqrt{\lambda }}{4\pi}\sim 1 $$ , with the error decreasing quickly at large ’t Hooft coupling. Furthermore, for the same structure constant we obtain a 4-loop analytic result at weak coupling. We also present results for excited states.

Abstract We complete the program of [1] about perturbative approaches for N $$ \mathcal{N} $$ = 2 superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of AdS 5 × S 5 with the aim of testing possible holographic perspectives of quiver theories in N $$ \mathcal{N} $$ = 2.

Abstract We consider a family of N $$ \mathcal{N} $$ = 2 superconformal field theories in four dimensions, defined as ℤ q orbifolds of N $$ \mathcal{N} $$ = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the N $$ \mathcal{N} $$ = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from N $$ \mathcal{N} $$ = 4 only at high orders in perturbation theory.

Abstract We compute the running coupling of non-Abelian gauge theories in the Schrödinger-functional scheme, by means of non-equilibrium Monte Carlo simulations on the lattice.

Abstract We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT4 proposed by Ö. Gürdŏgan and one of the authors as a double scaling limit of γ-deformed N Unknown character 0 x F 700 from " Euclid Math One " 0 x 3 D = 4 $$ \mathcal{N}\mathrm{Unknown}\ \mathrm{character}\ \left(0\mathrm{x}\mathrm{F}700\right)\ \mathrm{from}\ "\mathrm{Euclid}\ \mathrm{Math}\ \mathrm{One}"\ \left(0\mathrm{x}3\mathrm{D}\right) = 4 $$ SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized “dynamical fishnet” structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain four-point correlators in the full chiral CFT4, generalizing recent results for a particular one-coupling version of this theory — the bi-scalar “fishnet” CFT. We sum up exactly thecorresponding Feynman diagrams, including both bosonic and fermionic loops, by Bethe-Salpeter method. This provides explicit OPE data for various twist-2 operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.

Abstract In this paper we study the Bremsstrahlung functions for the 16BPS $$ \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} $$ and the 12BPS $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson lines in ABJM theory. First we use a superconformal defect approach to prove a conjectured relation between the Bremsstrahlung functions associated to the geometric (B 1/6 φ ) and R-symmetry (B 1/6 θ ) deformations of the 16BPS $$ \frac{1}{6}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson line. This result, non-trivially following from a defect supersymmetric Ward identity, provides an exact expression for B 1/6 θ based on a known result for B 1/6 φ . Subsequently, we explore the consequences of this relation for the 12BPS $$ \frac{1}{2}\mathrm{B}\mathrm{P}\mathrm{S} $$ Wilson line and, using the localization result for the multiply wound Wilson loop, we provide an exact closed form for the corresponding Bremsstrahlung function. Interestingly, for the comparison with integrability, this expression appears particularly natural in terms of the conjectured interpolating function h(λ). During the derivation of these results we analyze the protected defect supermultiplets associated to the broken symmetries, including their two- and three-point correlators.

Abstract We study operator insertions into 1/2 BPS Wilson loops in N $$ \mathcal{N} $$ = 6 ABJM theory and investigate their two-point correlators. In this framework, the energy emitted by a heavy moving probe can be exactly obtained from some two-point coefficients of bosonic and fermionic insertions. This allows us to confirm an early proposal [1] for computing the Bremsstrahlung function in terms of certain supersymmetric circular Wilson loops, whose value might be accessible to localization techniques. In the derivation of this result we also elucidate the structure of protected multiplets in the relevant superconformal defect theory and perform an explicit two-loop calculation.

Abstract We consider antiparallel Wilson lines in N $$ \mathcal{N} $$ = 4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines’ expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit.

Abstract We present the three-loop calculation of the Bremsstrahlung function associated to the 1/2-BPS cusp in ABJM theory, including color subleading corrections. Using the BPS condition we reduce the computation to that of a cusp with vanishing angle. We work within the framework of heavy quark effective theory (HQET) that further simplifies the analytic evaluation of the relevant cusp anomalous dimension in the near-BPS limit. The result passes nontrivial tests, such as exponentiation, and is in agreement with the conjecture made in [1] for the exact expression of the Bremsstrahlung function, based on the relation with fermionic latitude Wilson loops.