# Continuous Advances in QCD 2016

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Item Lessons from numerical holography(2016-05-13) Yaffe, LaurenceShow more Gauge/gravity duality (or “holography”) allows one to calculate highly non-trivial far from equilibrium dynamics in strongly coupledgauge theory --- provided one can solve asymptotically anti-deSitter initial value problems in higher dimensional gravity. Recent results and work in progress in this area will be discussed, focusing on calculations motivated by the physics of heavy ion collisions and thermal gauge theories.Show more Item How supersymmetry helps to understand hydrodynamics(2016-05-15) Koroteev, PeterShow more We discuss the connection between periodic finite-difference Intermediate Long Wave hydrodynamical systems and integrable many-body models of Calogero and Ruijsenaars-type. The former describe quantum cohomology and quantum K-theory of the ADHM moduli space of Abelian instantons, while the latter arise in the the instanton counting in four and five dimensional supersymmetric gauge theories with eight supercharges in the presence of defects. Using string theory dualities we provide correspondences between hydrodynamical and many-body integrable systems. In particular, we match the energy spectra on both sides.Show more Item Non-Abelian string of a finite length(2016-05-15) Monin, SergeyShow more We consider world-sheet theories for non-Abelian strings assuming compactification on a cylinder with a finite circumference $L$ and periodic boundary conditions. The dynamics of the orientational modes is described by two-dimensional CP$(N-1)$ model. We analyze both non-supersymmetric (bosonic) model and ${\mathcal N}=(2,2)$ supersymmetric CP$(N-1)$ emerging in the case of 1/2-BPS saturated strings in \ntwo supersymmetric QCD with $N_f=N$. The non-supersymmetric case was studied previously; technically our results agree with those obtained previously, although our interpretation is totally different. In the large-$N$ limit we detect a phase transition at $L\sim \Lambda_{\rm CP}^{-1}$ (which is expected to become a rapid crossover at finite $N$). If at large $L$ the CP$(N-1)$ model develops a mass gap and is in the Coulomb/confinement phase, with exponentially suppressed finite-$L$ effects, at small $L$ it is in the deconfinement phase, and the orientational modes contribute to the L\”usher term. The latter becomes dependent on the rank of the bulk gauge group. In the supersymmetric CP$(N-1)$ models at finite $L$ we find a large-$N$ solution which was not known previously. We observe a single phase independently of the value of $L\Lambda_{\rm CP}$. For any value of this parameter a mass gap develops and supersymmetry remains unbroken. So does the $SU(N)$ symmetry of the target space. The mass gap turns out to be independent of the string length. The L\”uscher term is absent due to supersymmetry.Show more Item Worldsheet-induced corrections to the holographic Veneziano amplitude(2016-05-15) Ireson, EdwinShow more Following an earlier result that recovered the Veneziano amplitude in the high-energy regime of Yang-Mills theories by the AdS/CFT correspondance, the natural next step forward is to investigate what kind of corrections we get as we change the energy scale. By allowing worldsheet fluctuations of the string hanging from the boundary, we obtain a qualitative first look at such effects.Show more Item Large-N CP(N-1) sigma model on a finite interval with the Dirichlet condition(2016-05-15) Ohashi, KeisukeShow more We study the large-N solution of the bosonic CP(N-1) model on a finite interval |with the Dirichlet conditions. In the literature, this model has been studied with translational invariant ansatz and there an existence of phase transition was found. |We find that this |translational invariant ansatz can not give a solution of the gap equation and |divergence behavior appears around the boundaries, and resultantly |the phase transition do not appear in this system.Show more Item Vortices in Neutron Superfluids(2016-05-15) Nitta, MunetoShow more Neutron triplet (3P2) superfluids are believed to realize in high density neutron matter such as the cores of neutron stars. I discuss topological aspects of neutron 3P2 superfluids such as integer vortices, half-quantized non-Abelian vortices and topological superfluidity. This talk is based on the work in collaboration with Kota Masuda and Takeshi Mizushima. |[1] K. Masuda and MN, Phys.Rev. C93 (2016) 035804 [arXiv:1512.01946 [nucl-th]].|[2] K. Masuda and MN,arXiv:1602.07050 [nucl-th] |[3] T. Mizushima, K. Masuda and MN, in preparation.Show more Item Critical string from non-Abelian vortex in four dimensions(2016-05-15) Yung, AlexeiShow more It is shown that non-Abelian string supported in N=2 supersymmetric QCD with U(N) gauge group and |number of quark multiplets 2N can behave as a fundamental superstring. In addition to translational moduli the non-Abelian string carry also orientational/ size moduli. Their dynamics is described by two dimensional weighted CP(N,N) model on the string world sheet. For N=2 the dimension of orientational/ size moduli space is six and can be combined with four translational moduli to form a ten dimensional space required for a superstring to be critical. For this case CP(2,2) model|on the string world sheet is defined on the non-compact Calabi-Yau conifold. We study the closed string states which emerges in four dimensions and identify them with mesons of the bulk theory. We find one massless hypermultiplet associated with the deformation of the complex structure of the conifold.Show more Item Low-Energy Effective Action of the Supersymmetric CP(N-1) Model in the Large-N Limit(2016-05-14) Bolokhov, PavelShow more Motivated by an old would-be paradox we found a solution of supersymmetric CP(N-1) models in superfields. Our main target is the Kahler potential, since the superpotential term was exactly known since early 1990s.To this end we used the large-N expansion to perform a supersymmetric calculation in the leading order in 1/N. |The models considered are N= (2,2) basic CP(N-1) model and its nonminimal N= (0,2) deformation various aspects of which are being actively studied since 2007. Another extension is solving the above models in the presence of nonvanishing twisted masses.Show more Item Toward a Theory of the QCD String(2016-05-14) Dubovsky, SergeiShow more We construct a new model of four-dimensional relativistic strings with integrable dynamics on the worldsheet. In addition to translational modes this model contains a single massless pseudoscalar worldsheet field - the worldsheet axion. The axion couples to a topological density which counts the self-intersection number of a string. The corresponding coupling is fixed by integrability to Qâ‰ˆ0.37. We argue that this model is a member of a larger family of relativistic non-critical integrable string models. This family includes and extends conventional non-critical strings described by the linear dilaton CFT. Intriguingly, recent lattice data in SU(3) and SU(5) gluodynamics reveals the presence of a massive pseudoscalar axion on the worldsheet of confining flux tubes. The value of the corresponding coupling, as determined from the lattice data, is equal to Q_Lâ‰ˆ0.38Â±0.04.Show more Item String pair production in non homogeneous backgrounds(2016-05-14) Bolognesi, StefanoShow more We consider string pair production in non homogeneous electric backgrounds. We study several particular configurations which can be addressed with the Euclidean world-sheet instanton technique, the analogue of the world-line instanton for particles. In the first case the string is suspended between two D-branes in flat space-time, in the second case the string lives in AdS and terminates on one D-brane (this realizes the holographic Schwinger effect). In some regions of parameter space the result is well approximated by the known analytical formulas, either the particle pair production in non-homogeneous background or the string pair production in homogeneous background. In other cases we see effects which are intrinsically stringy and related to the non-homogeneity of the background. The pair production is enhanced already for particles in time dependent electric field backgrounds. The string nature enhances this even further. For spacial varying electrical background fields the string pair production is less suppressed than the rate of particle pair production. We discuss in some detail how the critical field is affected by the non-homogeneity, for both time and space dependent electric field backgrounds, as well as an interesting new prediction for the small field limit. The third case we consider is pair production in holographic confining backgrounds with homogeneous and non-homogeneous fields.Show more Item Instanton-torus knot duality in SQCD(2016-05-14) Gorsky, AlexanderShow more Item Resurgence, exact WKB and quantum geometry(2016-05-14) Basar, GokceShow more The theory of resurgence connects high order terms of perturbative series to low order terms in non-perturbative sectors. In this talk I will present a different type of resurgent relation that connects perturbative and non-perturbative sectors in a term-by-term fashion in certain quantum mechanical systems. This relation is valid for everywhere in the spectrum and has a geometric interpretation in terms of quantization of Riemann surfaces. Notably, the spectra of these quantum mechanical examples encode the vacua of certain N=2 supersymmetric gauge theories in the Nekrasov-Shatashvili limit.Show more Item Toward Picard-Lefschetz Theory of Path Integrals and the Physics of Complex Saddles(2016-05-14) Unsal, MithatShow more We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory. |In the supersymmetric theories, the inclusion of complex saddles is strictly necessary to prevent clash with the supersymmetry algebra. In calculable Yang-Mills theories, the non-perturbative stabilization of center-symmetry is due to complex saddles, called neutral bions.Show more Item Resurgence and Large N(2016-05-14) Dunne, GeraldShow more I discuss the interplay between large N and strong and weak coupling expansions, in the context of resurgent asymptotics. Examples include quantum spectral problems, and related SUSY superpotentials, and the Gross-Witten-Wadia matrix model phase transition.Show more Item All order linearised hydrodynamics from fluid-gravity correspondence(2016-05-14) Lublinsky, MichaelShow more Relativistic fluid dynamics emerges as an effective theory describing strongly coupled QFTs at finite temperature. Following a brief intro into relativistic fluid dynamics, I will discuss how constitutive relation/transport coefficients of a fluid can be obtained using the holographic methods. Applying the fluid/gravity correspondence, we have determined the (linearized) stress energy tensor of Nîˆº=4 super-Yang-Mills theory at strong coupling accounting for all orders in derivatives of the fluid velocity. I will introduce momenta-dependent transport functions, such as generalized shear viscosity, and will derive closed form linear holographic RG|flow-type equations for these functions.Show more Item Dilaton, conformal symmetry and Weyl invariance(2016-05-14) Monin, AlexanderShow more Iâ€™ll show how to implement spontaneous breaking of conformal symmetry at the quantum level from the IR perspective. In other words how to introduce consistently the (massless) dilaton. Given the importance of the Weyl invariance in the construction it is necessary to understand the relation between conformal symmetry and Weyl invariance. I’ll touch upon the issue and present examples of theories that are conformally invariant but do not admit Weyl invariant generalizations.Show more Item Quantum corrections for the generators of conformal transformations in QCD(2016-05-14) Braun, VladimirShow more QCD evolution equations in minimal subtraction schemes have a hidden symmetry:|One can construct three operators that commute with the evolution kernel and form an SL(2) algebra,|i.e. they satisfy (exactly) the SL(2) commutation relations. In this work we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer d=4-2epsilon space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in d=4-2epsilon effectively correspond|to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators.|This approach is valid to all orders in perturbation theory and the result includes automatically all terms|that can be identified as due to a nonvanishing QCD beta-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet|quark-antiquark operators including mixing with the operators containing total derivatives.These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.Show more Item Approaching conformality in lattice models(2016-05-14) Meurice, YannickShow more We discuss new renormalization group methods designed to study near conformal situations in two dimensional spin models and four dimensional multi flavor gauge theories.Show more Item Continuous chiral symmetry breaking in a calculable regime(2016-05-14) Cherman, AlekseyShow more I will discuss work with M. Unsal on a semiclassically-calculable regime of 4D QCD, obtained by an adiabatic circle compactification, in which continuous chiral symmetry breaking can be studied systematically.Show more Item Correlations in hadronic wave function(2016-05-14) Kovner, AlexShow more I discuss within the Color Glass approach, how Bose-Einstein correlations between gluons in hadronic wave function can exhibit themselves as observable correlations between emitted particles in the final state.Show more

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