Non-perturbative Terms Research Articles

Modeling the nonperturbative contributions to the complex heavy-quark potential

In this paper, we construct a simple model for the complex heavy quark potential which is defined through the Fourier transform of the static gluon propagator. Besides the hard thermal loop resummed contribution, the gluon propagator also includes a non-perturbative term induced by the dimension two gluon condensate. Within the framework of thermal field theory, the real and imaginary parts of the heavy quark potential are determined in a consistent way without resorting to any extra assumption as long as the exact form of the retarded/advanced gluon propagator is specified. The resulting potential model has the desired asymptotic behaviors and reproduces the data from lattice simulation reasonably well. By presenting a direct comparison with other complex potential models on the market, we find the one proposed in this work shows a significant improvement on the description of the lattice results, especially for the imaginary part of the potential, in a temperature region relevant to quarkonium studies.

Surface operators in {mathcal N}=2 SQCD and Seiberg Duality

We study half-BPS surface operators in mathcal {N}=2 supersymmetric asymptotically conformal gauge theories in four dimensions with SU(N) gauge group and 2N fundamental flavours using localization methods and coupled 2d/4d quiver gauge theories. We show that contours specified by a particular Jeffrey–Kirwan residue prescription in the localization analysis map to particular realizations of the surface operator as flavour defects. Seiberg duality of the 2d/4d quivers is mapped to contour deformations of the localization integral which in this case involves a residue at infinity. This is reflected as a modified Seiberg duality rule that shifts the Lagrangian of the purported dual theory by non-perturbative terms. The new rules, that depend on the 4d gauge coupling, lead to a match between the low energy effective twisted chiral superpotentials for any pair of dual 2d/4d quivers.

Supersymmetric Dirac-Born-Infeld axionic inflation and non-Gaussianity

An analysis is given of inflation based on a supersymmetric Dirac-Born-Infeld (DBI) action in an axionic landscape. The DBI model we discuss involves a landscape of chiral superfields with one U(1) shift symmetry which is broken by instanton type non-perturbative terms in the superpotential. Breaking of the shift symmetry leads to one pseudo-Nambu-Goldstone-boson which acts as the inflaton while the remaining normalized phases of the chiral fields generically labeled axions are invariant under the U(1) shift symmetry. The analysis is carried out in the vacuum with stabilized saxions, which are the magnitudes of the chiral fields. Regions of the parameter space where slow-roll inflation occurs are exhibited and the spectral indices as well as the ratio of the tensor to the scalar power spectrum are computed. An interesting aspect of supersymmetric DBI models analyzed is that in most of the parameter space tensor to scalar ratio and scalar spectral index are consistent with Planck data if slow roll occurs and is not eternal. Also interesting is that the ratio of the tensor to the scalar power spectrum can be large and can lie close to the experimental upper limit and thus testable in improved experiment. Non-Gaussianity in this class of models is explored.

Updating [formula omitted] from SVZ-moments and their ratios

Using recent values of αs, the gluon condensates 〈αsG2〉 and 〈g3fabcG3〉 and the new data on the ψ/ϒ-families, we update our determinations of the MS‾ running quark masses m‾c,b(m‾c,b) from the SVZ-moments Mn(Q2) and their ratios [1,2] by including higher order perturbative (PT) corrections, non-perturbative (NPT) terms up to dimension d=8 and using the degree n-stability criteria of the (ratios of) moments. Optimal results from different (ratios of) moments converge to the accurate mean values: m‾c(m‾c)=1264(6)MeV and m‾b(m‾b)=4188(8)MeV in Table 4, which improve and confirm our previous findings [1,2] and the recent ones from Laplace sum rules [3]. Comments on some other determinations of m‾c(m‾c) and 〈αsG2〉 from the SVZ-(ratios of) moments in the vector channel are given in Section 5.

Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors

Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and the nonperturbative sectors. Then, we show that the dynamics in the deep multistreaming regime is governed by attractors. In the case of simple initial conditions, these attractors coincide with the asymptotic configurations of the adhesion model, but in general they may differ. These results are applied to a cosmological setting, and an algorithm to build the attractor solution starting from the Zel'dovich approximation is developed. Finally, this algorithm is applied to the search of `haloes' and the results are compared with those obtained from the exact dynamical equations.

Holographic CBK relation

The Crewther–Broadhurst–Kataev (CBK) relation connects the Bjorken function for deep-inelastic sum rules (or the Gross–Llewellyn Smith function) with the Adler function for electron–positron annihilation in QCD; it has been checked to hold up to four loops in perturbation theory. Here we study non-perturbative terms in the CBK relation using a holographic dual theory that is believed to capture properties of QCD. We show that for the large invariant momenta the perturbative CBK relation is exactly satisfied. For the small momenta non-perturbative corrections enter the relation and we calculate their significant effects. We also give an exact holographic expression for the Bjorken function, as well as for the entire three-point axial-vector–vector correlation function, and check their consistency in the conformal limit.

Evidence for inflation in an axion landscape

We discuss inflation models within supersymmetry and supergravity frameworks with a landscape of chiral superfields and one U(1) shift symmetry which is broken by non-perturbative symmetry breaking terms in the superpotential. We label the pseudo scalar component of the chiral fields axions and their real parts saxions. Thus in the models only one combination of axions will be a pseudo-Nambu-Goldstone-boson which will act as the inflaton. The proposed models constitute consistent inflation for the following reasons: the inflation potential arises dynamically with stabilized saxions, the axion decay constant can lie in the sub-Planckian region, and consistency with the Planck data is achieved. The axion landscape consisting of m axion pairs is assumed with the axions in each pair having opposite charges. A fast roll-slow roll splitting mechanism for the axion potential is proposed which is realized with a special choice of the axion basis. In this basis the 2m coupled equations split into 2m − 1 equations which enter in the fast roll and there is one unique linear combination of the 2m fields which controls the slow roll and thus the power spectrum of curvature and tensor perturbations. It is shown that a significant part of the parameter space exists where inflation is successful, i.e., Npivot = [50, 60], the spectral index ns of curvature perturbations, and the ratio r of the power spectrum of tensor perturbations and curvature perturbations, lie in the experimentally allowed regions given by the Planck experiment. Further, it is shown that the model allows for a significant region of the parameter space where the effective axion decay constant can lie in the sub-Planckian domain. An analysis of the tensor spectral index nt is also given and the future experimental data which constraints nt will further narrow down the parameter space of the proposed inflationary models. Topics of further interest include implications of the model for gravitational waves and non-Gaussianities in the curvature perturbations. Also of interest is embedding of the model in strings which are expected to possess a large axionic landscape.

Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds

We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by Beasley and Witten shows that these instanton contributions cancel among curves within a given homology class for Calabi-Yau manifolds that can be described as hypersurfaces or complete intersections in projective or toric ambient spaces. We provide a prescription that identifies all ℙ1 curves in certain homology classes of complete intersection Calabi-Yau manifolds in products of projective spaces (CICYs) and cross-check our results by a comparison with the genus zero Gromov-Witten invariants. We then use this construction to study instanton superpotentials on those manifolds and their quotients. We identify a non-toric quotient of a non-favorable CICY with a single genus zero curve in a certain homology class, so that a cancellation à la Beasley-Witten is not possible. In another example, we study a non-toric quotient of a favorable CICY and check that the superpotential still vanishes. From this and related examples, we conjecture that the Beasley-Witten cancellation result can be extended to toric and non-toric quotients of CICYs, but can be avoided if the CICY is non-favorable.

Modular symmetry in magnetized/intersecting D-brane models

We study the modular symmetry in four-dimensional low-energy effective field theory, which is derived from type IIB magnetized D-brane models and type IIA intersecting D-brane models. We analyze modular symmetric behaviors of perturbative terms and non-perturbative terms induced by D-brane instanton effects. Anomalies are also investigated and such an analysis on anomalies suggests corrections in effective field theory.

Resurgence of the dressing phase for AdS5 \xd7 S5

We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the AdS5 × S5 superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious.

Mellin–Barnes Representation of the Topological String

We invoke integrals of Mellin-Barnes type to analytically continue the Gopakumar-Vafa resummation of the topological string free energy in the string coupling constant, leading to additional non-perturbative terms. We also discuss in a similar manner the refined and Nekrasov-Shatashvili limit version thereof. The derivation is straight-forward and essentially boils down to taking residue. This allows us to confirm some related conjectures in the literature at tree-level.

Quarkonium dissociation in an anisotropic QGP

We have studied the properties of quarkonium states in an anisotropic quark-gluon plasma (QGP). We address the effects of non-perturbative confining force and momentum anisotropy on the heavy quark potential at finite temperature, which have been resolved by correcting both perturbative and non-perturbative terms of the Cornell potential through the dielectric function in terms of hard-loop resumed gluon propagator in real-time formalism. We have found that the real-part of the potential becomes stronger and thus makes the quarkonia more bound whereas the (magnitude) imaginary-part too becomes larger and thus contribute more to the thermal width, compared to the medium-contribution of the Coulomb term alone. In addition, the presence of anisotropy makes the real-part of the potential stronger but the imaginary-part is weakened slightly. The potential obtained in anisotropic medium is nonspherical. Therefore, we have used the first-order perturbation theory to estimate the shift in energy eigenvalues due to the small anisotropic correction to the energy eigenvalues from the spherically-symmetric part in isotropic medium and determine their dissociation temperatures. The presence of non-perturbative term in the potential results the quarkonia to dissociate at higher temperatures.

Un-oriented quiver theories for Majorana neutrons

In the context of un-oriented open string theories, we identify quivers whereby a Majorana mass for the neutron is indirectly generated by exotic instantons. We discuss two classes of (Susy) Standard Model like quivers, depending on the embedding of SU(2)_W in the Chan-Paton group. In both cases, the main mechanism involves a vector-like pair mixing through a non-perturbative mass term. We also discuss possible relations between the phenomenology of Neutron-Antineutron oscillations and LHC physics in these models. In particular, a vector-like pair of color-triplet scalars or color-triplet fermions could be directly detected at LHC, compatibly with n-\bar{n} limits. Finally we briefly comment on Pati-Salam extensions of our models.

Natural inflation and moduli stabilization in heterotic orbifolds

We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio r ≈ 0.05. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedekind η function. We present two setups inspired by the mini-landscape models of the ℤ6 − II orbifold which realize aligned inflation and stabilization of the relevant moduli. One has a supersymmetric vacuum after inflation, while the other includes a gaugino condensate which breaks supersymmetry at a high scale.

Complex potential and bottomonium suppression at LHC energy

We have studied the thermal suppression of the bottomonium states in relativistic heavy-ion collision at LHC energies as function of centrality, rapidity, transverse momentum. First, we address the effects of the nonperturbative confining force and the momentum anisotropy together on heavy quark potential at finite temperature, which are resolved by correcting both the perturbative and nonperturbative terms of the potential at T = 0 in a weakly-anisotropic medium, not its perturbative term alone as usually done in the literature. Second, we model the expansion of medium by the Bjorken hydrodynamics in the presence of both shear and bulk viscosity, followed by an additional pre-equilibrium anisotropic evolution. Finally, we couple them together to quantify the yields of bottomonium production in nucleus–nucleus collisions at LHC energies and found a better agreement with the CMS data. Our estimate of the inclusive ϒ(1S) production indirectly constrains both the uncertainties in isotropization time and the shear-to-entropy density ratio and favors the values as 0.3 fm/c and 0.3 (perturbative result), respectively.

Imaginary part of the medium modified heavy quark potential

We have calculated the dissociation of quarkonia through an imaginary potential which is obtained by correcting both the perturbative and non-perturbative terms of the potential at T=0 through the dielectric function in real-time formalism. The real-part of the potential becomes stronger and thus makes the quarkonia more bound whereas the (magnitude) imaginary-part too becomes larger and thus contribute more to the thermal width, compared to the medium-contribution of the Coulomb term alone. We have also extended our calculation to anisotropic medium, by calculating the leading anisotropic corrections to the propagators in Keldysh representation. The presence of anisotropy makes the real-part of the potential stronger but the imaginary-part is weakened slightly and the competition between them results in higher dissociation temperatures compared to isotropic medium.

A perturbative renormalization group approach to driven quantum systems

We use a perturbative momentum shell renormalization group (RG) approach to study the properties of a driven quantum system at zero temperature. To illustrate the technique, we consider a bosonic ϕ4 theory with an arbitrary time dependent interaction parameter λ(t) = λ f(ω0t), where ω0 is the drive frequency and we derive the RG equations for the system using a Keldysh diagrammatic technique. We show that the scaling of ω0 is analogous to that of temperature for a system in thermal equilibrium and its presence provides a cutoff scale for the RG flow. We analyze the resultant RG equations, derive an analytical condition for such a drive to take the system out of the gaussian regime, and show that the onset of the non-gaussian regime occurs concomitantly with the appearance of non-perturbative mode coupling terms in the effective action of the system. We supplement the above-mentioned results by obtaining them from equations of motion of the bosons and discuss their significance for systems near critical points described by time-dependent Landau-Ginzburg theories.

Density‐matrix theory of quantum dynamics under a strong external field switched on nonadiabatically

Quantum time‐evolution equations for the density matrix are formulated in the unrestricted Hartree–Fock approximation, with an emphasis on the nonperturbative effect due to a sudden or gradual onset of a strong external field. Numerical simulations are performed for ideal Fermi gas around a square‐well potential which is switched on dynamically. When the switching is fast enough, an oscillatory motion of the particle is induced by a nonadiabatic transition at the Landau–Zener crossing point, which is most clearly seen in a small‐size system. When the switching is sufficiently slow, the simulation corroborates the adiabatic theorem. It is shown that the Anderson's infrared catastrophe in a metal is strongly enhanced by the nonperturbative effect. The Keldysh formula of atomic multiphoton ionization can also be derived from the nonperturbative term in the density‐matrix equation, indicating a wide applicability of the present theory. © 2014 Wiley Periodicals, Inc.

Dissociation of quarkonium in a complex potential

We have studied the quasi-free dissociation of quarkonia through a complex potential which is obtained by correcting both the perturbative and nonperturbative terms of the $Q \bar Q$ potential at T=0 through the dielectric function in real-time formalism. The presence of confining nonperturbative term even above the transition temperature makes the real-part of the potential more stronger and thus makes the quarkonia more bound and also enhances the (magnitude) imaginary-part which, in turn contributes more to the thermal width, compared to the medium-contribution of the perturbative term alone. These cumulative observations result the quarkonia to dissociate at higher temperatures. Finally we extend our calculation to a medium, exhibiting local momentum anisotropy, by calculating the leading anisotropic corrections to the propagators in Keldysh representation. The presence of anisotropy makes the real-part of the potential stronger but the imaginary-part is weakened slightly. However, since the medium corrections to the imaginary-part is a small perturbation to the vacuum part, overall the anisotropy makes the dissociation temperatures higher, compared to isotropic medium.

Delineating parton distributions and the strong coupling

Global fits for precision determinations of parton distributions, together with the highly correlated strong coupling ${\ensuremath{\alpha}}_{s}$, are presented up to next-to-next-to-leading order (NNLO) of QCD utilizing most world data (charm and jet production data are used where theoretically possible), except Tevatron gauge boson production data and LHC data which are left for genuine predictions. This is done within the ``dynamical'' (valence-like input at ${Q}_{0}^{2}=0.8\text{ }\text{ }{\mathrm{GeV}}^{2}$) and ``standard'' (input at ${Q}_{0}^{2}=2\text{ }\text{ }{\mathrm{GeV}}^{2}$) approach. The stability and reliability of the results are ensured by including nonperturbative higher-twist terms, nuclear corrections as well as target mass corrections, and by applying various (${Q}^{2}$, ${W}^{2}$) cuts on available data. In addition, the ${Q}_{0}^{2}$ dependence of the results is studied in detail. Predictions are given, in particular for the LHC, for gauge- and Higgs-boson as well as for top-quark pair production. At NNLO the dynamical approach results in ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1136\ifmmode\pm\else\textpm\fi{}0.0004$, whereas the somewhat less constrained standard fit gives ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})=0.1162\ifmmode\pm\else\textpm\fi{}0.0006$.