On one-loop corrections in the standard model effective field theory; the Γ( h → γγ ) case

We calculate one loop contributions to Γ( h → γγ ) from higher dimensional operators in the Standard Model Effective Field Theory (SMEFT). Some technical challenges related to determining Electroweak one loop “finite terms” are discussed and overcome. Although we restrict our attention to Γ( h → γγ ), several developments we report have broad implications. Firstly, the running of the vacuum expectation value (vev) modifies the log( μ ) dependence of processes in a manner that is not captured in some past SMEFT Renormalization Group (RG) calculations. Secondly, higher dimensional operators can source ghost interactions in R ξ gauges due to a modified gauge fixing procedure. Lastly, higher dimensional operators can contribute with pure finite terms at one loop in a manner that is not anticipated in a RG analysis. These results cast recent speculation on the nature of one loop corrections in the SMEFT in an entirely new light

Partitioning Composite Finite Systems

We compare different analytical and numerical methods for studying the partitions of a finite system into fragments. We propose a new numerical method of exploring the partition space by generating the Markov chains of partitions based on the Metropolis algorithm. The advantages of the new method for the problems where partitions are sampled with non-trivial weights are demonstrated

Viscous asymptotically flat Reissner-Nordström black branes

We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p -brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and the brane is thus Gregory-Laflamme unstable as expected. For sufficiently large values of the charge, the sound mode becomes stable, however, in this regime the hydrodynamic mode associated with charge diffusion is found to be unstable. The electrically charged brane is thus found to be (classically) unstable for all values of the charge density in agreement with general thermodynamic arguments. Finally, we show that the shear viscosity to entropy bound is saturated, as expected, while the proposed bounds for the bulk viscosity to entropy can be violated in certain regimes of the charge of the brane

Spin Matrix theory: a quantum mechanical model of the AdS/CFT correspondence

We introduce a new quantum mechanical theory called Spin Matrix theory (SMT). The theory is interacting with a single coupling constant g and is based on a Hilbert space of harmonic oscillators with a spin index taking values in a Lie (super)algebra representation as well as matrix indices for the adjoint representation of U( N ). We show that SMT describes N = 4 $$\mathcal{N}=4$$ super-Yang-Mills theory (SYM) near zero-temperature critical points in the grand canonical phase diagram. Equivalently, SMT arises from non-relativistic limits of N = 4 $$\mathcal{N}=4$$ SYM. Even though SMT is a non-relativistic quantum mechanical theory it contains a variety of phases mimicking the AdS/CFT correspondence. Moreover, the g → ∞ limit of SMT can be mapped to the supersymmetric sector of string theory on AdS 5 × S 5 . We study SU(2) SMT in detail. At large N and low temperatures it is a theory of spin chains that for small g resembles planar gauge theory and for large g a non-relativistic string theory. When raising the temperature a partial deconfinement transition occurs due to finite- N effects. For sufficiently high temperatures the partially deconfined phase has a classical regime. We find a matrix model description of this regime at any coupling g . Setting g = 0 it is a theory of N 2 + 1 harmonic oscillators while for large g it becomes 2 N harmonic oscillators

Large N lattice QCD and its extended strong-weak connection to the hypersphere

We calculate an effective Polyakov line action of QCD at large N c and large N f from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S 1 × S d at weak coupling from one loop perturbation theory, and find that a large N c correspondence of equations of motion found in [1] at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward

A note on the Lee–Yang singularity coupled to 2d quantum gravity

We show how to obtain the critical exponent of magnetization in the Lee–Yang edge singularity model coupled to two-dimensional quantum gravity

Unitarity cuts of integrals with doubled propagators

We extend the notion of generalized unitarity cuts to accommodate loop integrals with higher powers of propagators. Such integrals frequently arise in for example integration-by-parts identities, Schwinger parametrizations and Mellin-Barnes representations. The method is applied to reduction of integrals with doubled and tripled propagators and direct extract of integral coefficients at one and two loops. Our algorithm is based on degenerate multivariate residues and computational algebraic geometry

Scattering equations and Feynman diagrams

We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in φ 3 -theory. We also discuss the generalization to general scalar field theories with φ p interactions, corresponding to polygonal graphs involving vertices of order p . Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands

Lifshitz space–times for Schrödinger holography

We show that asymptotically locally Lifshitz space–times are holographically dual to field theories that exhibit Schrödinger invariance. This involves a complete identification of the sources, which describe torsional Newton–Cartan geometry on the boundary and transform under the Schrödinger algebra. We furthermore identify the dual vevs from which we define and construct the boundary energy–momentum tensor and mass current and show that these obey Ward identities that are organized by the Schrödinger algebra. We also point out that even though the energy flux has scaling dimension larger than z+2 , it can be expressed in terms of computable vev/source pairs

Integration rules for scattering equations

As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints fo any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory