Related papers: The Analytic Bootstrap in Fermionic CFTs
Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal…
Non-linear integral equations derived from Bethe Ansatz are used to evaluate finite size corrections to the highest (i.e. {\it anti-ferromagnetic}) and immediately lower anomalous dimensions of scalar operators in ${\cal N}=4$ SYM. In…
Multi-critical behavior of interacting fermions in graphene's honeycomb lattice is presented. In particular, we considered the spin triplet insulating orders, where the spin rotational symmetry of the order parameter is explicitly broken.…
We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866, arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction.…
We compute the anomalous dimensions of a class of operators of the form $(\bar\psi\psi)^p$ and $(\bar\psi\psi)^p\psi$ to leading order in $\epsilon$ in the Gross-Neveu model in $2+\epsilon$ dimensions. We use the techniques developed in…
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…
We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE,…
We review 2d CFT in the bootstrap approach, and sketch the known exactly solvable CFTs with no extended chiral symmetry: Liouville theory, (generalized) minimal models, limits thereof, and loop CFTs, including the $O(n)$, Potts and $PSU(n)$…
For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary…
We reinterpret and extend some old work on CFT/string duality. We consider some asymptotically conformal field theory in large N limit, with conformal symmetry broken by VEV's of infinite number of operators. Assuming that this theory…
We study numerically on the lattice the 2D Yukawa model with the U(1) chiral symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling behaviour of the fermion mass, as the Yukawa coupling approaches zero, is analysed…
We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non…
We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion (OPE), without assuming unitarity. We find the minimal models as special cases, as well as additional…
The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we…
The constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions. The prescriptions can be applied to both unitary and non unitary theories allowing for the study of the spectrum of…
We construct a fermionic lattice model containing interacting spin-$\frac{1}{2}$ fermions with an $O(4)$ symmetry. In addition the model contains a $\mathbb{Z}_2$ chiral symmetry which prevents a fermion mass term. Our model is motivated by…
We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the…
We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for…