Walking in the SU(N)

We study the phase diagram as function of the number of colours and flavours of asymptotically free non-supersymmetric theories with matter in higher dimensional representations of arbitrary SU(N) gauge groups. Since matter in higher dimensional representations screens more than in the fundamental a general feature is that a lower number of flavours is needed to achieve a near-conformal theory. We study the spectrum of the theories near the fixed point and consider possible applications of our analysis to the dynamical breaking of the electroweak symmetry.Comment: 12 page

Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $L^1_{loc}$) to the unique Kruzkov entropy solution of the conservation law. The initial data are taken in $L^1\cap L^\infty$, nonnegative, and with compact support, hence we are able to handle densities with vacuum. Our result holds for a reasonably general class of velocity maps (including all the relevant examples in the applications, e.g. in the Lighthill-Whitham-Richards model for traffic flow) with possible degenerate slope near the vacuum state. The proof of the result is based on discrete BV estimates and on a discrete version of the one-sided Oleinik-type condition. In particular, we prove that the regularizing effect $L^1\cap L^\infty \mapsto BV$ for nonlinear scalar conservation laws is intrinsic of the discrete model

Linear growth of the trace anomaly in Yang-Mills thermodynamics

In the lattice work by Miller [1,2] and in the work by Zwanziger [3] a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. These results show the remarkable property that the corresponding systems are strong interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with [1,2,3]Comment: 9 pages and 2 figure

General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization

We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabilizable, along with an explicit procedure for constructing Markovian dynamics that achieve stabilization. If the target state is not full-rank, we establish sufficiency under an additional condition, which is naturally motivated by consistency with pure-state stabilization results yet provably not necessary in general. Several applications are discussed, of relevance to both dissipative quantum engineering and information processing, and non-equilibrium quantum statistical mechanics. In particular, we show that a large class of graph product states (including arbitrary thermal graph states) as well as Gibbs states of commuting Hamiltonians are frustration-free stabilizable relative to natural quasi-locality constraints. Likewise, we provide explicit examples of non-commuting Gibbs states and non-trivially entangled mixed states that are stabilizable despite the lack of an underlying commuting structure, albeit scalability to arbitrary system size remains in this case an open question.Comment: 44 pages, main results are improved, several proofs are more streamlined, application section is refine

Integrability of the quantum KdV equation at c = -2

We present a simple a direct proof of the complete integrability of the quantum KdV equation at $c=-2$, with an explicit description of all the conservation laws.Comment: 9 page