Related papers: Four-Fermion Theory and the Conformal Bootstrap
We study the instabilities to the conformal critical point of an exactly solvable family of Gross-Neveu models. Using conformal field theory techniques, we construct the zero-temperature phase diagram and identify the superconducting and…
Near conformal dynamics is employed in different extensions of the standard model of particle interactions as well as in cosmology. Many of its interesting properties are either conjectured or determined using model computations. We…
We discuss the chiral symmetry restoration at high temperature and chemical potential for a four-fermion interaction theory in arbitrary dimensions ($2\leq D<4$). To investigate the ground state of the theory we calculate the effective…
We study a set of large-$N$ tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised…
The critical behavior of a non-local scalar field theory is studied. This theory has a non-local quartic interaction term which involves a real power -\beta of the Laplacian. The parameter \beta can be tuned so as to make that interaction…
We investigate the role of four-fermion interactions, rotational and particle-hole asymmetries, and their interplay in three-dimensional systems with a quadratic band touching point by virtue of the renormalization group approach, which…
We study a system of fermions interacting with a scalar field, in 4+1 dimensions where the 5th dimension is compactified, using an exact functional method, where quantum fluctuations are controlled by the amplitude of the bare fermion mass.…
A number of 2d and 3d four-fermion models which are renormalizable ---in the $1/N$ expansion--- in a maximally symmetric constant curvature space, are investigated. To this purpose, a powerful method for the exact study of spinor heat…
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from…
Incorporated with twisted boundary condition, Polyakov loop correlators can give a definition of the renormalized coupling. We employ this scheme for the step scaling method (with step size s = 2) in the search of conformal fixed point of…
We present explicit recursive relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the…
Based on the spectrum identified in our earlier work [arXiv:1809.02191], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the $Q$-state Potts model. Crucial in our…
We study the Gross-Neveu-Yukawa field theory for the SO($N$) symmetric traceless rank-two tensor order parameter coupled to Majorana fermions using the $\epsilon$-expansion around upper critical dimensions of $3+1$ to two loops. Previously…
The renormalization group transformation for the hierarchical O(N) spin model in four dimensions is studied by means of characteristic functions of single-site measures, and convergence of the critical trajectory to the Gaussian fixed point…
Under the assumption that degenerate fields exist, diagonal CFTs such as Liouville theory can be solved analytically using the conformal bootstrap method. Here we generalize this approach to non-diagonal CFTs, i.e. CFTs whose primary fields…
We examine the fixed point behaviour of Yukawa couplings in supersymmetric theories with varying numbers of dimensions. We show that Pendleton-Ross fixed point behaviour is greatly amplified in the MSSM with no extra dimensions and 4 extra…
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in $D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve…
We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits…
We search for asymptotic safety in a Yukawa system with a chiral $U(N_L)_L\otimes U(1)_R$ symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative…
The critical behavior of a relativistic $\mathbb{Z}_2$-symmetric Yukawa model at zero temperature and density is discussed for a continuous number of fermion degrees of freedom and of spacetime dimensions, with emphasis on the role played…