We show that the so-called λ deformed σ-model as well as the η deformed one belong to a class of the E-models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ ...solely by the choice of the Drinfeld double; for the λ model the double is the direct product G×G while for the η model it is the complexified group GC. As a consequence of this picture, we prove for any G that the target space geometries of the λ-model and of the Poisson–Lie T-dual of the η-model are related by a simple analytic continuation.
It turns out that many integrable σ-models on group manifolds belong to the class of the so-called E-models which are relevant in the context of the Poisson–Lie T-duality. We show that this is the ...case also for the Yang–Baxter σ-model with WZNW term introduced by Delduc, Magro and Vicedo in 5.
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function ...with respect to a stationary equilibrium state, we employ asymptotic analysis to infer the structure of charge current fluctuations for a continuous range of timescales. The solution exhibits several unorthodox features. Most prominently, on the timescale of typical fluctuations the probability distribution of the integrated charge current in a stationary ensemble without bias is distinctly non-Gaussian despite diffusive behavior of dynamical charge susceptibility. While inducing a charge imbalance is enough to recover Gaussian fluctuations, we find that higher cumulants grow indefinitely in time with different exponents, implying singular scaled cumulants. We associate this phenomenon with the lack of a regularity condition on moment generating functions and the onset of a dynamical critical point. In effect, the scaled cumulant generating function does not, irrespectively of charge bias, represent a faithful generating function of the scaled cumulants, yet the associated Legendre dual yields the correct large-deviation rate function. Our findings hint at novel types of dynamical universality classes in deterministic many-body systems.
String theory is one of the most active branches of theoretical physics and has the potential to provide a unified description of all known particles and interactions. This book is a systematic ...introduction to the subject, focused on the detailed description of how string theory is connected to the real world of particle physics. Aimed at graduate students and researchers working in high energy physics, it provides explicit models of physics beyond the Standard Model. No prior knowledge of string theory is required as all necessary material is provided in the introductory chapters. The book provides particle phenomenologists with the information needed to understand string theory model building and describes in detail several alternative approaches to model building, such as heterotic string compactifications, intersecting D-brane models, D-branes at singularities and F-theory.
We consider a chain consisting of n+1 pinned harmonic oscillators subjected on the right to a time dependent periodic force F(t) while Langevin thermostats are attached at both endpoints of the ...chain. We show that for long times the system is described by a Gaussian measure whose covariance function is independent of the force, while the means are periodic. We compute explicitly the work and energy due to the periodic force for all n including n → ∞.
Canonical bases for cluster algebras GROSS, MARK; HACKING, PAUL; KEEL, SEAN ...
Journal of the American Mathematical Society,
04/2018, Volume:
31, Issue:
2
Journal Article
Peer reviewed
Open access
In an earlier work (Publ. Inst. Hautes Études Sci., 122 (2015), 65-168) the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties ...(those with maximal boundary) has a canonical vector space basis parameterized by the integral tropical points of the mirror. Further, the structure constants for the multiplication rule in this basis should be given by counting broken lines (certain combinatorial objects, morally the tropicalizations of holomorphic discs). Here we prove the conjecture in the case of cluster varieties, where the statement is a more precise form of the Fock-Goncharov dual basis conjecture (Publ. Inst. Hautes Études Sci., 103 (2006), 1-211). In particular, under suitable hypotheses, for each Y the partial compactification of an affine cluster variety U given by allowing some frozen variables to vanish, we obtain canonical bases for H^0(Y,\mathcal {O}_Y) extending to a basis of H^0(U,\mathcal {O}_U). Each choice of seed canonically identifies the parameterizing sets of these bases with integral points in a polyhedral cone. These results specialize to basis results of combinatorial representation theory. For example, by considering the open double Bruhat cell U in the basic affine space Y, we obtain a canonical basis of each irreducible representation of \operatorname {SL}_r, parameterized by a set which each choice of seed identifies with the integral points of a lattice polytope. These bases and polytopes are all constructed essentially without representation-theoretic considerations. Along the way, our methods prove a number of conjectures in cluster theory, including positivity of the Laurent phenomenon for cluster algebras of geometric type.
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