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

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

Exact stabilization of entangled states in finite time by dissipative quantum circuits

Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly non-canonical) commuting parent Hamiltonian may be found. Beside graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi. Extensions to representative classes of mixed graph-product and thermal states are also discussed.Comment: 20 + 9 pages, 9 figure