Recursions for rational q,t-Catalan numbers

We give a simple recursion labeled by binary sequences which computes rational q,t-Catalan power series, both in relatively prime and non relatively prime cases. It is inspired by, but not identical to recursions due to B. Elias, M. Hogancamp, and A. Mellit, obtained in their study of link homology. We also compare our recursion with the Hogancamp-Mellit's recursion and verify a connection between the Khovanov-Rozansky homology of N,M-torus links and the rational q,t-Catalan power series for general positive N,M

Affine permutations and rational slope parking functions

We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to two previously known combinatorial constructions: Haglund’s bijection ζ exchanging the pairs of statistics (area, dinv) and (bounce, area) on Dyck paths, and the Pak-Stanley labeling of the regions of k-Shi hyperplane arrangements by k-parking functions. Essentially, our approach can be viewed as a generalization and a unification of these two constructions. We also relate our combinatorial constructions to representation theory. We derive new formulas for the Poincaré polynomials of certain affine Springer fibers and describe a connection to the theory of finite-dimensional representations of DAHA and non-symmetric Macdonald polynomials

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.Comment: 17 page

Nonabelian Strings and Axion

We address two distinct but related issues: (i) the impact of (two-dimensional) axions in a two-dimensional theory known to model confinement, the CP(N-1) model; (ii) bulk axions in four-dimensional Yang-Mills theory supporting non-Abelian strings. In the first case n, \bar n kinks play the role of "quarks." They are known to be confined. We show that introduction of axions leads to deconfinement (at very large distances). This is akin to the phenomenon of wall liberation in four-dimensional Yang-Mills theory. In the second case we demonstrate that the bulk axion does not liberate confined (anti)monopoles, in contradistinction with the two-dimensional model. A novel physical effect which we observe is the axion radiation caused by monopole-antimonopole pairs attached to the non-Abelian strings.Comment: 16 pp, 4 figure

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.Comment: 11 pages, 1 figur