Related papers: O(N)-Universality Classes and the Mermin-Wagner Th…
I review the Thirring model in 2+1$d$ dimensions, focussing in particular on possible strongly-interacting UV-stable fixed points of the renormalisation group, corresponding to a continuous phase transition where a U($2N$) global symmetry…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well…
Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor…
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…
In this paper, we study a double scaling limit of two multi-matrix models: the $U(N)^2 \times O(D)$-invariant model with all quartic interactions and the bipartite $U(N) \times O(D)$-invariant model with tetrahedral interaction ($D$ being…
We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows…
We analyze the $\mathcal{N}=1$ supersymmetric Wess-Zumino model dimensionally reduced to the $\mathcal{N}=2$ supersymmetric model in three Euclidean dimensions. As in the original model in four dimensions and the $\mathcal{N}=(2,2)$ model…
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+\omega})$, as $N$ tends to infinity. For Wigner matrices this…
Let D be a division ring such that the number of conjugacy classes in the multiplicative group D^* is equal to the power of D^*. Suppose that H(V) is the group GL(V) or PGL(V), where V is an infinite-dimensional vector space over D. We…
We renormalize models with scalar chiral superfields with an odd superpotential to several orders in perturbation theory. These extensions of the cubic Wess-Zumino model are renormalizable in spacetime dimensions which are rational. When…
We elucidate a non-conserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a non-zero noise cross-correlation of amplitude $D_\times$ in a stochastic Langevin…
In the last few years the derivative expansion of the Non-Perturbative Renormalization Group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of…
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…
We study three dimensional N=2 supersymmetric QCD theories with O(N_c) gauge groups and with N_f chiral multiplets in the vector representation. We argue that for N_f < N_c-2 there is a runaway potential on the moduli space and no vacuum.…
We examine the statistics of conformations of a linear polymer in a solvent. The polymer is allowed to form double polymers. We closely follow a classical technique to derive a field theory for the problem from an $O\left(n\right)$…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral…
A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation…
Complex Wadati-type potentials of the form $V(x)=-w^2(x) + iw_x(x)$, where $w(x)$ is a real-valued function, are known to possess a number of intriguing features, unusual for generic non-Hermitian potentials. In the present work, we…