The effective actions of gauge bosons, fermions and scalars, which are obtained within the hard-loop approximation, are shown to have unique forms for a whole class of gauge theories including QED, scalar QED, super QED, pure Yang-Mills, QCD, super Yang-Mills. The universality occurs irrespective of a field content of each theory and of variety of specific interactions. Consequently, the long-wavelength or semiclassical features of plasma systems governed by these theories such as collective excitations are almost identical. An origin of the universality, which holds within the limits of applicability of the hard-loop approach, is discussed.
Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the lit…
We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has been checked against partial results available in the literature. The broad applicability of this approach simplifies one-loop matching from an ultraviolet model to a lower-energy effective field theory (EFT), a procedure which is now reduced to the evaluation of a combination of matrices in our universal expression, without any loop integrals to evaluate. W…
Recently, a general result for evaluating the path integral at one loop was obtained in the form of the Universal One-Loop Effective Action. It may be used to derive effective field theory operators of dimensions up to six, by evaluating the traces of matrices in this expression, with the mass-dependence encapsulated in the universal coefficients. Here we show that it can account for loops of mixed heavy-light particles in the matching procedure. Our prescription for computing these mixed contributions to the Wilson coefficients is conceptually simple. Moreover it has the advantage of maintain…
We extend useful properties of the $H\toγγ$ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form -- regardless of the nature of the internal particle -- still holds at this order. We also present an algorithmic way to renormalise two-loop amplitudes, by locally cancelling the ultraviolet singularities at integrand level, thus allowing a full four-dimensional numerical implementation of the method. Our results are compared with analytic expressions already available in the literature,…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with the reduction problem of one-loop integrals with general tensor structures as well as propagators with arbitrary higher powers. In this paper, we show that how to combine Feynman parametrization and embedding formalism to give a universal treatment of reductions for general one-loop integrals, even including the degenerated cases, such as the vanishing Gram …
The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recentl…
We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills model. These results are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 agree with the predictions obtained from the BFKL equation for N=4 SYM in the next-to-leading order. The asymptotics of universal anomalous dimension at large j is in an agreement with the expectations based on an interpolation between weak and strong coupling regi…
We compute the non-planar contribution to the universal anomalous dimension of twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin eighteen. Exploiting the results of this and our previous calculations along with recent analytic results for the cusp anomalous dimension and some expected analytic properties, we reconstruct a general expression valid for arbitrary Lorentz spin. We study various properties of this general result, such as its large-spin limit, its small-x limit, and others. In particular, we present a prediction for the non-planar contrib…
The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these calculations, some ingredients remain specially challenging. This is the case of multiloop scattering amplitudes that constitute a hard bottleneck to solve. In this paper, we delve into the application of a disruptive technique based on the loop-tree duality theorem, which is aimed at an efficient computation of such objects by opening the loops to nondisjoint trees…
We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string -- M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of th…
The effective actions of gauge bosons, fermions and scalars, which are obtained within the hard-loop approximation, are shown to have unique forms for a whole class of gauge theories including QED, scalar QED, super QED, pure Yang-Mills, QCD, super Yang-Mills. The universality occurs irrespective of a field content of each theory and of variety of specific interactions. Consequently, the long-wavelength or semiclassical features of plasma systems governed by these theories such as collective excitations are almost identical. An origin of the universality, which holds within the limits of appli…
Inspired by recent progress on classical limits of scattering amplitudes, we show that hard thermal loops can be obtained from classical limits of off-shell currents. The classicality of hard thermal loops is made manifest by associating classical wavenumbers to soft particles. We compute the classical limit of these currents in QED, QCD and gravity. Our proposal does not involve the introduction of ghosts.
The self-interacting $λϕ^{4}$ scalar field theory is a warhorse in quantum field theory. Here we explore the one-loop order impact from one universal extra dimension, $S^{1}/\mathbb{Z}_{2}$, to the self-energy and four point vertex functions associated to this theory. Such effects come as an infinite number of UV divergences corresponding to an infinite superposition of excited KK particles around the loop. We show that dimensional regularisation is adequate enough to control them in terms of the product of the one dimensional inhomogenous Epstein zeta function times the gamma function. From t…
We compute the four-loop corrections to the Higgs-bottom vertex within massless QCD and present analytic results for all color structures. The infrared poles of the renormalized form factor agree with the predicted four-loop pattern. Furthermore, we use the results for the Higgs-bottom, photon-quark, and Higgs-gluon form factors to provide hard matching coefficients in soft-collinear effective theory up to four-loop accuracy.
We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the nonplanar contribution to the four-loop lightlike cusp anomalous dimension and derive the transcendental $ζ_3$ and $ζ_5$ parts of the universal anomalous dimension for arbitrary Lorentz spin in analytic form. As for the lightlike cusp anomalous dimension and the $ζ_5$ part of the universal anomalous dimension, we confirm previous results.
We present the result of a full direct component calculation for the term proportional to zeta(5) in the four-loop universal anomalous dimension of the twist-2 operators in N =4 supersymmetric Yang-Mills theory for the first three even moments. We suggest the general form such contribution for the arbitrary Lorentz spin of the twist-2 operators.
We investigate strongly correlated non-Abelian plasmas out of equilibrium. Based on numerical simulations, we establish a self-similar scaling property for the time evolution of spatial Wilson loops that characterizes a universal state of matter far from equilibrium. Most remarkably, it exhibits a generalized area law which holds for sufficiently large ratio of spatial area and fractional power of time. Performing calculations also for the perturbative regime at higher momenta, we are able to characterize the full nonthermal scaling properties of SU(2) and SU(3) symmetric plasmas from short to…
We study loop corrections to the universal dilaton supermultiplet for type IIA strings compactified on Calabi-Yau threefolds. We show that the corresponding quaternionic kinetic terms receive non-trivial one-loop contributions proportional to the Euler number of the Calabi-Yau manifold, while the higher-loop corrections can be absorbed by field redefinitions. The corrected metric is no longer Kahler. Our analysis implies in particular that the Calabi-Yau volume is renormalized by loop effects which are present even in higher orders, while there are also one-loop corrections to the Bianchi iden…
The hard thermal loop effective action for Goldstone bosons is deduced by symmetry arguments from the corresponding result for gauge bosons. Pseudoscalar mesons in Chromodynamics and magnons in an antiferromagnet are discussed as special cases, including the hard thermal loop contribution to their scattering.
The Real Projective Plane is the lowest dimensional orbifold which, when combined with the usual Minkowski space-time, gives rise to a unique model in six flat dimensions possessing an exact Kaluza Klein (KK) parity as a relic symmetry of the broken six dimensional Lorentz group. As a consequence of this property, any model formulated on this background will include a stable Dark Matter candidate. Loop corrections play a crucial role because they remove mass degeneracy in the tiers of KK modes and induce new couplings which mediate decays. We study the full one loop structure of the correction…
We present a simple, new method for the 1-loop renormalization of integrable $σ$-models. By treating equations of motion and Bianchi identities on an equal footing, we derive 'universal' formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a 'completeness' condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles …
We present results for Wilson loops in strongly coupled gauge theories. The loops may be taken around an arbitrarily shaped contour and in any field theory with a dual IIB geometry of the form M x S^5. No assumptions about supersymmetry are made. The first result uses D5 branes to show how the loop in any antisymmetric representation is computed in terms of the loop in the fundamental representation. The second result uses D3 branes to observe that each loop defines a rich sequence of operators associated with minimal surfaces in S^5. The action of these configurations are all computable. Both…
We show that the high temperature limit of the noncommutative thermal Yang-Mills theory can be directly obtained from the Boltzmann transport equation of classical particles. As an illustration of the simplicity of the Boltzmann method, we evaluate the two and the three-point gluon functions in the noncommutative U(N) theory at high temperatures T. These amplitudes are gauge invariant and satisfy simple Ward identities. Using the constraint satisfied at order T^2 by the covariantly conserved current, we construct the hard thermal loop effective action of the noncommutative theory.
The universal hypermultiplet arises as a subsector of every Calabi-Yau compactification of M-theory or Type II string theory. Classically its moduli space is the quaternionic space $SU(2,1)/U(2)$. We show that this moduli space receives a one-loop correction proportional to the Euler character of the Calabi-Yau, which can locally be absorbed by a certain constant shift of the fields. The correction vanishes in the limit that the Planck mass is taken to infinity, and hence is essentially gravitational in nature.
CP violation by soft supersymmetry-breaking terms in orbifold compactifications is investigated. We include the universal part of the moduli-dependent threshold corrections in the construction of the non-perturbative effective potential due to gaugino-condensation. This allows interpolation of the magnitude of CP violating phases between the weakly and strongly coupled regimes. We find that the universal threshold corrections have a large effect on the CP violating phases in the weakly coupled regime.
We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory. These expressions are obtained by extracting the most complicated contributions from the three-loop anomalous dimensions in QCD. This result is in an agreement with the hypothesis of the integrability of N=4 Supersymmetric Yang-Mills theory in the context of AdS/CFT-correspondence.
The flavor dependence of the QCD phase diagram presents universal properties in the heavy quark limit. For the wide class of models where the quarks are treated at the one-loop level, we show, for arbitrary chemical potential, that the flavor dependence of the critical quark masses-for which the confinement-deconfinement transition is second order-is insensitive to the details of the (confining) gluon dynamics and that the critical temperature is constant along the corresponding critical line. We illustrate this with explicit results in various such one-loop models studied in the literature: e…
We present a conjecture for the normalisation of the twist two conformal partial waves in a double OPE limit of the four-point function of stress tensor multiplets in N = 4 super Yang-Mills theory up to three loops. This contains information about the structure constants in the OPE. Like the twist two anomalous dimensions our result is expressed as a linear combination of harmonic sums whose argument is the spin of the exchanged operators. To arrive at the result we derive asymptotic expansions for the twist two part of two unknown three-loop integrals using the method of expansion by regions,…
Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one. In the functional momentum representation the obtained equation decouples into two independent ones, which describe the dynamics of the transverse and longitudinal components of the area derivative of the Wilson loop. At some critical value of the momentum discontinuity, which can be determined from a certain equation, the transverse component does not propagate…
We study, in the imaginary-time formalism, the high temperature behavior of n-point thermal loops in static Yang-Mills and gravitational fields. We show that in this regime, any hard thermal loop gives the same leading contribution as the one obtained by evaluating the loop at zero external energies and momenta.
We present the result of a full direct component calculation for the non-planar contribution to the four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. The result contains only zeta(5) term and is proportional to zeta(5) contribution in the planar case, which comes purely from wrapping corrections. We have extended also our previous calculations for the leading transcendental contribution arXiv:0811.0607 on non-planar case and have found the same results up to a common factor. It allows us to suggest that the non-planar contribution to the four-loop …
We consider finite temperature 1-loop diagrams with hard loop momenta and an arbitrary number of external gauge fields when the external momenta are either soft, or near the light cone and nearly collinear with the loop momentum. We obtain a recursion relation for these diagrams which we translate into an equation for their generating functional. By integrating out the soft fields while keeping two collinear ones we find an integral equation, originally due to Arnold, Moore, and Yaffe, which sums the bremsstrahlung and pair annihilation contribution to the thermal photon production rate.
We examine, through a Boltzmann equation approach, the generating action of hard thermal loops in the background of gravitational fields. Using the gauge and Weyl invariance of the theory at high temperature, we derive an explicit closed-form expression for the effective action.
I review recent developments in QCD thermodynamics and collective excitations from the hard-thermal-loop effective theory. I begin by motivating the discussion with open questions from heavy-ion collisions. I then discuss a finite-temperature and -density calculation of QCD thermodynamics at NNLO from the hard-thermal-loop perturbation theory. Finally I discuss a recent exploration of generalizing the hard-thermal-loop framework to the (chromo)magnetic scale $g^2T$, from which a novel massless mode is uncovered.
We discuss the high temperature behavior of retarded thermal loops in static external fields. We employ an analytic continuation of the imaginary time formalism and use a spectral representation of the thermal amplitudes. We show that, to all orders, the leading contributions of static hard thermal loops can be directly obtained by evaluating them at zero external energies and momenta.
We use the background field method along with a special gauge condition, to derive the hard thermal loop effective action in a simple manner. The new point in the paper is to relate the effective action explicitly to the S-matrix from the onset.
We derive a closed form expression for the long wavelength limit of the effective action for hard thermal loops in an external gravitational field. It is a function of the metric, independent of time derivatives. It is compared and contrasted with the static limit, and with the corresponding limits in an external Yang-Mills field.
We study, in the long wave-length and static limits, the structure of the n-point graviton functions at high temperature. Using the gauge and Weyl invariance of the theory, we derive a simple expression for the hard thermal amplitudes in these two limits.
We investigate the use of the hard thermal loop (HTL) resummation technique in non-equilibrium field theory. We use the Keldysh representation of the real time formalism (RTF). We derive the HTL photon self energy and the resummed photon propagator. We show that no pinch singularities appear in the non-equilibrium HTL effective propagator. We discuss a possible regularization mechanism for these singularities at higher orders. As an example of the application of the HTL resummation method within the RTF we discuss the damping rate of a hard electron.
The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading logarithmic term. Inspired by the success of one-loop quantum gravity for computing the logarithmic corrections to black hole entropy, we try to reproduce this universal term by a one-loop calculation in Euclidean eleven-dimensional supergravity on AdS_4 \times X_7. We find perfect agreement between the results of ABJM theory and the eleven dimensional supergravity.
We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional phi3 theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.
We give a classifying theory for $LG$-bundles, where $LG$ is the loop group of a compact Lie group $G$, and present a calculation for the string class of the universal $LG$-bundle. We show that this class is in fact an equivariant cohomology class and give an equivariant differential form representing it. We then use the caloron correspondence to define (higher) characteristic classes for $LG$-bundles and to prove for the free loop group an analogue of the result for characteristic classes for based loop groups in Murray-Vozzo (J. Geom. Phys., 60(9), 2010). These classes have a natural interpr…
We construct a family of Poisson structures of hydrodynamic type on the loop space of $\mathbb{C} P^{n-1}$. This family is parametrized by the moduli space of elliptic curves or, in other words, by the modular parameter $τ$. This family can be lifted to a homogeneous Poisson structure on the loop space of $\mathbb{C}^n$ but in order to do that we need to upgrade the modular parameter $τ$ to an additional field $τ(x)$ with Poisson brackets $\{τ(x),τ(y)\}=0,~~\{τ(x),z_a(y)\}=2πi~ z_a(y)~δ^{\prime}(x-y)$ where $z_1,...,z_n$ are coordinates on $\mathbb{C}^n$. These homogeneous Poisson structures c…
The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths for eigenvalues are arbitrary homology classes of paths for which the integral is convergent. This choice includes in particular the case where the integration path has fixed endpoints, called hard edges. The hard edges induce boundary contributions in the loop equations. The purpose of this article is to give the loop equations in that semicassical setting.
