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Register a new userElectrostatics of Coulomb gas, lattice paths, and discrete polynuclear growth
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We study the partition function of a two-dimensional Coulomb gas on a circle, in the presence of external pointlike charges, in a double scaling limit where both the external charges and the number of gas particles are large. Our original motivation comes from studying amplitudes for multi-string emission from a decaying D-brane in the high energy limit. We analyze the scaling limit of the partition function and calculate explicit results. We also consider applications to random matrix theory. The partition functions can be related to random scattering, or to weights of lattice paths in certain growth models. In particular, we consider the discrete polynuclear growth model and use our results to compute the cumulative probability density for the height of long level-1 paths. We also obtain an estimate for an almost certain maximum height.
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We study the high-energy limit of tree-level string production amplitudes from decaying D-branes in bosonic string theory, interpreting the vertex operators as external charges interacting with a Coulomb gas corresponding to the rolling tachyon background, and performing an electrostatic analysis. In particular, we consider two open string - one closed string amplitudes and four open string amplitudes, and calculate explicit formulas for the leading exponential behavior.
We study four-dimensional Chern-Simons theory on $D times mathbb{C}$ (where $D$ is a disk), which is understood to describe rational solutions of the Yang-Baxter equation from the work of Costello, Witten and Yamazaki. We find that the theory is dual to a boundary theory, that is a three-dimensional analogue of the two-dimensional chiral WZW model. This boundary theory gives rise to a current algebra that turns out to be an analytically-continued toroidal Lie algebra. In addition, we show how certain bulk correlation functions of two and three Wilson lines can be captured by boundary correlation functions of local operators in the three-dimensional WZW model. In particular, we reproduce the leading and subleading nontrivial contributions to the rational R-matrix purely from the boundary theory.
We elucidate how integrable lattice models described by Costellos 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.
We present a lattice formulation of noncommutative Yang-Mills theory in arbitrary even dimensionality. The UV/IR mixing characteristic of noncommutative field theories is demonstrated at a completely nonperturbative level. We prove a discrete Morita equivalence between ordinary Yang-Mills theory with multi-valued gauge fields and noncommutative Yang-Mills theory with periodic gauge fields. Using this equivalence, we show that generic noncommutative gauge theories in the continuum can be regularized nonperturbatively by means of {it ordinary} lattice gauge theory with t~Hooft flux. In the case of irrational noncommutativity parameters, the rank of the gauge group of the commutative lattice theory must be sent to infinity in the continuum limit. As a special case, the construction includes the recent description of noncommutative Yang-Mills theories using twisted large $N$ reduced models. We study the coupling of noncommutative gauge fields to matter fields in the fundamental representation of the gauge group using the lattice formalism. The large mass expansion is used to describe the physical meaning of Wilson loops in noncommutative gauge theories. We also demonstrate Morita equivalence in the presence of fundamental matter fields and use this property to comment on the calculation of the beta-function in noncommutative quantum electrodynamics.
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed models are simplifi
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