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We show how to obtain the ultraviolet central charge from the exact S-matrix for a wide variety of models with a $U(1)$ symmetry. This is done by coupling the $U(1)$ current $J$ to a background field. In an $N$=2 superconformal theory with…
We study families of one-dimensional CFTs relevant for describing gapped QFTs in AdS$_2$. Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge from the flat space limit of CFT correlators. In this limit we prove…
We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…
The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and…
In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which…
Conformal field theories (CFTs) with MN and tetragonal global symmetry in $d=2+1$ dimensions are relevant for structural, antiferromagnetic and helimagnetic phase transitions in a wide class of materials. The study of these theories with…
We consider the critical $O(N)$ model in the presence of an external magnetic field localized in space. This setup can potentially be realized in quantum simulators and in some liquid mixtures. The external field can be understood as a…
We investigate $O(N)$ boundary conformal field theories (BCFTs) with boundary interactions in $d=4-\epsilon$ and $d=3-\epsilon$ employing the analytic bootstrap. By deriving universal constraints on conformal data, we show that infinitely…
In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a…
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…
In this letter, we consider effective field theories for light fields transforming under the fundamental or adjoint representation of a continuous group. We demonstrate that in the presence of gravity, crossing symmetry combined with two…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(\phi^i \phi^i)^2$. For $2<d<4$ these theories flow to the Wilson-Fisher fixed points for any $N$. A standard large $N$ Hubbard-Stratonovich…
A theory with a non-compact form-symmetry is described by two closed form fields of degrees k and d-k. Effective theory examples are non-linear electrodynamics, a photon field coupled to a neutron field, and a low energy Goldstone boson. We…
We explore the sum over topologies in AdS$_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal…
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG…
Generalising a result of classical mechanics an infinite set of conserved quantities can be found for the bare equations of motion describing the evolution of a scalar field in out of equilibrium quantum field theory, in the large N…
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…