54 research outputs found
Screening Currents Ward Identity and Integral Formulas for the WZNW Correlation Functions
We derive, based on the Wakimoto realization, the integral formulas for the
WZNW correlation functions. The role of the ``screening currents Ward
identity'' is demonstrated with explicit examples. We also give a more simple
proof of a previous result.Comment: 26 page
Exchange Relations for the q-Vertex Operators of
We consider the q-deformed Knizhnik-Zamolodchikov equation for the two point
function of q-deformed vertex operators of . We give explicitly the
fundamental solutions, the connection matrices and the exchange relations for
the q-vertex operators of spin 1/2 and .
Consequently, we confirm that the connection matrices are equivalent to the
elliptic Boltzman weights of IRF type obtained by the fusion procedure from ABF
models.Comment: 20p
Five-dimensional AGT Relation and the Deformed beta-ensemble
We discuss an analog of the AGT relation in five dimensions. We define a
q-deformation of the beta-ensemble which satisfies q-W constraint. We also show
a relation with the Nekrasov partition function of 5D SU(N) gauge theory with
N_f=2N.Comment: 38page. References and an appendix for 4D case added. Typos correcte
On the Quantization of Nambu Brackets
We present several non-trivial examples of the three-dimensional quantum
Nambu bracket which involve square matrices or three-index objects. Our
examples satisfy two fundamental properties of the classical Nambu bracket:
they are skew-symmetric and they obey the Fundamental Identity. We contrast our
approach to the existing literature on the quantum deformations of Nambu
mechanics. We also discuss possible applications of our results in M-theory.Comment: 18 pages, LaTeX fil
Volume conjecture: refined and categorified
The generalized volume conjecture relates asymptotic behavior of the colored Jones polynomials to objects naturally defined on an algebraic curve, the zero locus of the A-polynomial A(x,y). Another âfamily versionâ of the volume conjecture depends on a quantization parameter, usually denoted q or ħ; this quantum volume conjecture (also known as the AJ-conjecture) can be stated in a form of a q-difference equation that annihilates the colored Jones polynomials and SL(2,C) Chernâ Simons partition functions. We propose refinements/categorifications of both conjectures that include an extra deformation parameter t and describe similar properties of homological knot invariants and refined BPS invariants. Much like their unrefined/decategorified predecessors, that correspond to t=â1, the new volume conjectures involve objects naturally defined on an algebraic curve A^(ref)(x,y;t) obtained by a particular deformation of the A-polynomial, and its quantization Ă^(ref)(xË,Ć·;q,t). We compute both classical and quantum t-deformed curves in a number of examples coming from colored knot homologies and refined BPS invariants
Macdonald operators and homological invariants of the colored Hopf link
Using a power sum (boson) realization for the Macdonald operators, we
investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the
homological invariants of the colored Hopf link, which include
Khovanov-Rozansky homology as a special case. We prove the polynomiality of the
invariants obtained by GIKV's proposal for arbitrary representations. We derive
a closed formula of the invariants of the colored Hopf link for antisymmetric
representations. We argue that a little amendment of GIKV's proposal is
required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi
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