Anomalous Zero Sound
We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.
hep-th↗
arXiv subjects
A. Gorsky
Publications and source records attributed to A. Gorsky.
Baryon as dyonic instanton
We discuss the baryon in the holographic QCD framework and focus on the role of the bifundamental scalar field, realizing chiral symmetry breaking. We suggest the interpretation of a baryon as a dyonic instanton within the Atiyah-Manton-like approach for the flavor gauge group in the peculiar cylindrical ansatz in five-dimensional theory. Our approach provides the new mechanism of the stabilization of the baryon size.
hep-th↗
From elongated spanning trees to vicious random walks
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-ν} \log r$ with $ν= (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $ν$ is converting into the scaling exponent for the reunion probability (at a given point) of $k$ (1+1)--dimensional vicious walkers, $\tildeν = k^2/2$. Also, we express the conjectures about the possible relation to integrable systems.
cond-mat.stat-mech↗
Random ballistic growth and diffusion in symmetric spaces
Sequential ballistic deposition (BD) with next-nearest-neighbor (NNN) interactions in a N-column box is viewed a time-ordered product of N\times N-matrices consisting of a single sl_2-block which has a random position along the diagonal. We relate the uniform BD growth with the diffusion in the symmetric space H_N=SL(N,R)/SO(N). In particular, the distribution of the maximal height of a growing heap is connected with the distribution of the maximal distance for the diffusion process in H_N. The coordinates of H_N are interpreted as the coordinates of particles of the one--dimensional Toda chain. The group-theoretic structure of the system and links to some random matrix models are also discussed.
math-ph↗
More on the Tensor Response of the QCD Vacuum to an External Magnetic Field
In this Letter we discuss a few issues concerning the magnetic susceptibility of the quark condensate and the Son-Yamamoto (SY) anomaly matching equation. It is shown that the SY relation in the IR implies a nontrivial interplay between the kinetic and WZW terms in the chiral Lagrangian. It is also demonstrated that in a holographic framework an external magnetic field triggers mixing between scalar and tensor fields. Accounting for this, one may calculate the magnetic susceptibility of the quark condensate to all orders in the magnetic field.
hep-ph↗
Anomalous QCD Contribution to the Debye Screening in an External Field via Holography
In this paper we discuss the QCD contribution to the Abelian Debye and magnetic screening masses in a deconfined QCD plasma at finite temperature in the presence of an external magnetic field B. We use a holographic AdS/QCD setup in an AdS Schwarzschield black hole background and show that the electric screening mass has a form similar to the one-loop result in QED. Moreover, we calculate the corrections due to the magnetic field to all orders of B and demonstrate that in the case when magnetic field is large the Debye mass grows linearly with B, while the magnetic screening mass vanishes. The whole effect of the magnetic field turns out to stem from the Chern-Simons action. We also discuss the zero temperature case in the chiral perturbation theory.
hep-ph↗
Angular Momentum and Gravimagnetization of the ${\cal N}=2$ SYM vacuum
In this note we discuss the gravimagnetization of the ${\cal N}=2$ SYM vacuum in the $Ω$-background. It is argued that the Seiberg-Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean $R^4$ space. The possible role of the dyonic instantons as the microscopic angular momentum carriers which could yield the spontaneous vacuum gravimagnetization is conjectured. We interpret the dyonic instanton as a kind of the Euclidean bounce in $R^4$ similar to one responsible for the Schwinger pair creation. The induced angular momentum in $R^4$ is also briefly considered in the dual Liouville formulation of $SU(2)$ theory via AGT relation.
hep-th↗
Low-Energy Theorems from Holography
In the context of gauge/gravity duality, we verify two types of gauge theory low-energy theorems, the dilation Ward identities and the decoupling of heavy flavor. First, we provide an analytic proof of non-trivial dilation Ward identities for a theory holographically dual to a background with gluon condensate (the self-dual Liu--Tseytlin background). In this way an important class of low-energy theorems for correlators of different operators with the trace of the energy-momentum tensor is established, which so far has been studied in field theory only. Another low-energy relationship, the so-called decoupling theorem, is numerically shown to hold universally in three holographic models involving both the quark and the gluon condensate. We show this by comparing the ratio of the quark and gluon condensates in three different examples of gravity backgrounds with non-trivial dilaton flow. As a by-product of our study, we also obtain gauge field condensate contributions to meson transport coefficients.
hep-th↗
Confined Magnetic Monopoles in Dense QCD
Non-Abelian strings exist in the color-flavor locked phase of dense QCD. We show that kinks appearing in the world-sheet theory on these strings, in the form of the kink-antikink bound pairs, are the magnetic monopoles --- descendants of the 't Hooft-Polyakov monopoles surviving in such a special form in dense QCD. Our consideration is heavily based on analogies and inspiration coming from certain supersymmetric non-Abelian theories. This is the first ever analytic demonstration that objects unambiguously identifiable as the magnetic monopoles are "native" to non-Abelian Yang-Mills theories (albeit our analysis extends only to the phase of the monopole confinement and has nothing to say about their condensation). Technically our demonstration becomes possible due to the fact that low-energy dynamics of the non-Abelian strings in dense QCD is that of the orientational zero modes. It is described by an effective two-dimensional CP(2) model on the string world sheet. The kinks in this model representing confined magnetic monopoles are in a highly quantum regime.
hep-ph↗
On the Chiral Magnetic Effect in Soft-Wall AdS/QCD
The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan et al. within the Sakai--Sugimoto model, where it was shown to be zero. As an alternative, we calculate the chiral magnetic effect in soft-wall AdS/QCD and find a non-zero result with the natural boundary conditions. The mechanism of the dynamical neutralization of the chiral chemical potential via the string production is discussed in the dual two-form representation.
hep-ph↗
Remarks on Decay of Defects with Internal Degrees of Freedom
We consider the decay of metastable walls and strings populated by additional degrees of freedom. The examples involve the decay of an axion wall in an external magnetic field, pionic walls, metastable walls in dense QCD. It is shown that the induced fermions escape from the wall during the decay process providing an example of the chiral magnetic effect. An absolute stabilization of metastable and unstable walls in a large magnetic field is found. A possible higher dimensional generalization of the chiral magnetic effect is mentioned.
hep-th↗
Aspects of the N=4 SYM amplitude -- Wilson polygon duality
We discuss formulation of Wilson polygon - MHV amplitude duality at the perturbative level in various regularizations. For four gluons it is shown that at one loop one can formulate diagrammatic correspondence interpolating between the dimensional regularization and the off-shell one. We suggest new interpretation of all types of box diagrams in terms of the dual simplex in dimensional regularization and describe its degeneration to the Wilson polygon. The interesting nullification phenomena for the low-energy amplitudes in the Higgsed phase has been found.
hep-th↗
Correlator of Wilson and t'Hooft Loops at Strong Coupling in $\mathcal{N}=4$ SYM Theory
We calculate the correlator of a 't Hooft and a Wilson coplanar circular concentric loops at strong coupling in N=4 SYM theory when it reduces to the calculation of the composite minimal surface in the curved space with the proper boundary conditions. The minimal admissible ratio of the radii of 't Hooft and Wilson loops for such a configuration is found to be $\mathrm{e}^{-1/2}\approx 0.606$ at zero temperature and the dependence of the minimal admissible radii ratio on temperature is derived. At low temperatures the minimal admissible ratio for 't Hooft and Wilson loops remains close to 0.6, whereas at high temperatures $T$ it becomes equal to $\frac{1}{πT}$. We find that at any temperature there exists a phase transition point: beneath some specific value of 't Hooft loop radius the dual counterpart of Wilson-'t Hooft correlator is organized as two disconnected surfaces in AdS, whereas for 't Hooft loop radius above it, there exists a connected configuration with a junction of monopole, charge and dyon surfaces. We suggest a generalization of the entanglement entropy for charged boundaries and make some comments on its calculation at strong coupling.
hep-th↗
One-loop derivation of the Wilson polygon - MHV amplitude duality
We discuss the origin of the Wilson polygon - MHV amplitude duality at the perturbative level. It is shown that the duality for the MHV amplitudes at one-loop level can be proven upon the peculiar change of variables in Feynman parametrization and the use of the relation between Feynman integrals at the different space-time dimensions. Some generalization of the duality which implies the insertion of the particular vertex operator at the Wilson triangle is found for the 3-point function. We discuss analytical structure of Wilson loop diagrams and present the corresponding Landau equations. The geometrical interpretation of the loop diagram in terms of the hyperbolic geometry is discussed.
hep-th↗
Holographic Hadro-Quarkonium
We consider the recently suggested model for some resonances near the open charm threshold as bound states of charmonium inside excited light mesons. It is argued in the soft-wall holographic model of QCD that such states of heavy quarkonium necessarily exist at sufficiently large spin of the light meson. The bound state is provided by the dilaton exchange through the 5D bulk. We also argue that the decay of such bound systems into mesons with open heavy flavors due to splitting of the heavy quarkonium can be treated as semiclassical tunneling and is suppressed. This behavior is in agreement with the known relative suppression of the decay of the discussed charmonium-like resonances into channels with D mesons.
hep-th↗
Nonabelian strings in a dense matter
We consider gauge theories with scalar matter with and without supersymmetry at nonzero chemical potential. It is argued that a chemical potential plays a role similar to the FI term. We analyze theory at weak coupling regime at large chemical potential and argue that it supports nonabelian non-BPS strings. Worldsheet theory on the nonabelian string in a dense matter is briefly discussed.
hep-th↗
Magnetic strings in Lattice QCD as Nonabelian Vortices
Lattice studies indicate existence of magnetic strings in QCD vacuum. We argue that recently found nonabelian strings with rich worldsheet dynamics provide a proper pattern for the strings observed on the lattice. In particular, within this pattern we explain the localization of the monopole-antimonopole pairs on the magnetic string worldsheet and the negative contribution of the magnetic strings into the vacuum energy and gluon condensate. We suggest the D2 brane realization of the magnetic string which explains the temperature dependence of its tension.
hep-th↗
Supersymmetric Quantum Chromodynamics: How Confined Non-Abelian Monopoles Emerge from Quark Condensation
We consider N =1 supersymmetric QCD with the gauge group U(N) and N_f=N quark flavors. To get rid of flat directions we add a meson superfield. The theory has no adjoint fields and, therefore, no 't Hooft-Polyakov monopoles in the quasiclassical limit. We observe a non-Abelian Meissner effect: condensation of color charges (squarks) gives rise to confined monopoles. The very fact of their existence in N =1 supersymmetric QCD without adjoint scalars was not known previously. Our analysis is analytic and is based on the fact that the N =1 theory under consideration can be obtained starting from N =2 SQCD in which the 't Hooft-Polyakov monopoles do exist, through a certain limiting procedure allowing us to track the status of these monopoles at various stages. Monopoles are confined by BPS non-Abelian strings (flux tubes). Dynamics of string orientational zero modes are described by supersymmetric CP(N-1) sigma model on the string world sheet. If a dual of N =1 SQCD with the gauge group U(N) and N_f=N quark flavors could be identified, in this dual theory our demonstration would be equivalent to the proof of the non-Abelian dual Meissner effect.
hep-th↗