The color-flavor transformation for the unitary group (Zirnbauer 1996) is extended to the special unitary group. The resulting partition function is represented as sum over disconnected sectors characterized by a U(1)-charge. Application to low energy QCD on a lattice leads to a theory where the inverse number of colors appears as expansion parameter. We use a saddle point approximation to esti...

In general partition function form games, the recursive core coalition structure may be either coarser or finer than the one that maximizes the social surplus. Moreover, the recursive core structure is typically different from the one predicted by the α-core. We fully implement the recursive core for general games, including non-superadditive games where the grand coalition does not form in equ...

We present the construction of the partition function of 3-dimensional gravity in the Lorentzian regime as a state sum model over a triangulation. This generalize the work of Ponzano and Regge to the case of Lorentzian signature.

The Nekrasov conjecture predicts a relation between the partition function for N = 2 supersymmetric Yang–Mills theory and the Seiberg-Witten prepotential. For instantons on R, the conjecture was proved, independently and using different methods, by Nekrasov-Okounkov, Nakajima-Yoshioka, and Braverman-Etingof. We prove a generalized version of the conjecture for instantons on noncompact toric sur...

Abstract We study the form of the Turaev-Viro partition function Z(M) for different 3-manifolds with boundary. We show that for S2 boundaries Z(M) factorizes into a term which contains the boundary dependence and another which depends only on the topology of the underlying manifold. From this follows easily the formula for the connected sum of two manifolds Z(M#N ). For general Tg boundaries th...

We propose a class of sharing schemes for the distribution of the gains from cooperation for coalition games with externalities. In the context of the partition function, it is shown that any member of this class of sharing schemes leads to the same set of stable coalitions in the sense of d’Aspremont et al. (1983). These schemes are “almost ideal” in that they stabilize these coalitions which ...

On gauge fields-strings duality as an integrable system. Abstract It was suggested in [1], that semiclassically, a partition function of a string theory in the 5 dimensional constant negative curvature space with a boundary condition at the absolute satisfy the loop equation with respect to varying the boundary condition, and thus the partition function of the string gives the expectation value...

This article discusses partition function of monatomic ideal gas which is given in Statistical Physisc at Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Students in general are not familiar with partition function. This unfamiliarness was detected at a problem of partition function which was re-given in an examination in other dimensions ...

New formulas for the multiplicative partition function are developed. Besides giving a fast algorithm for generating these partitions, new identities for additive partitions and the Riemann zeta function are also produced.

We provide new characterization results for the value of games in partition function form. In particular, we use the potential of a game to define the value. We also provide a characterization of the class of values which satisfies one form of reduced game consistency.