The usual state-operator correspondence in Non Relativistic CFT maps the positively charged operators to the states in a harmonic trap. We point out that there exists a notion of state-operator correspondence which levarages the SL(2,R) subgroup of Schrodinger group and can be used to extend the state-operator map to the sector with zero charge. We can rederive the unitarity bounds using this...
The conformal data of CFTs involving heavy charged operators can be organised as a series in inverse powers of the global charges involved. When extrapolating these expansions to light low-charge sectors, it is relevant to ask whether these series are divergent and Borel-summable. In this talk, I will show that, generically, one would expect large-charge expansions to be divergent faster than...
In this talk I systematically study spinning correlators of a
generic non-parity violating CFT, with an O(2) internal symmetry at
sectors of large charge. At the beginning I will show the equivalence
between canonical and path integral quantization to the leading order
result, and subsequently I will use the former to compute three- and
four-point functions with conserved current...
I will review the applications of the fixed-charge semiclassical method to various models
concentrating mostly on the perturbative aspects of the calculation.
I will elucidate the identification of the lowest-lying operator, analytic structure of the large charge expansion and application to various proposed dualities at the critical point. I will conclude with several open problems.
In this talk, I will focus on two different methods that allow us to go beyond standard perturbation theory: the large charge expansion and resurgence. In particular, I will talk about the scaling dimension associated to charged operators in the O(N) model near d=4 and d=3 and monopoles operators in QED3. I will present their analytic structure for large and small values of the charge and...
I will discuss the large-charge expansion in cases where more than one charge is taken to be large.
As an illustration, I will consider the first known example of a Standard Model-like theory featuring asymptotic safety in four dimensions. In particular, I will present the contribution to the scaling dimension of charged operators stemming from quartic, Yukawa, and gauge interactions, and...
I will discuss the large-charge expansion of the conformal dimension Δ(Q) of the lowest operator of charge Q in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an external harmonic trap that confines the particles to a spherical cloud, at the edge of which the effective theory breaks down and leads to divergences. I will show how to...
Using large charge methods we evaluate the contributions from gauge invariant interactions to the scalar field anomalous dimensions in various models between 2 and 4 dimensions. Examples contain scalar QED, Nambu-Jona-Lasinio and Gross-Neveu-Yukawa models. In some of these, superconformal field theories emerge at the fixed points, exhibiting a rich structure and relation between actions...
We explore the quantum nature of black holes by introducing an effective frame- work that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild geometry in a way that is consistent with the physical scales of the black hole and its classical symmetries. This is achieved by organizing the quantum...
There are special classes of N=2 superconformal field theories in four dimensions, such as those of the “Argyres-Douglas” type, that feature an intrinsically strong dynamics. Due to the lack of a Lagrangian description, determining their properties quantitatively is a challenge. In this talk, I will present a general formula, which, inspired by the techniques of localization in gauge theory,...
I will argue for the instability of the O(N) Wilson-Fisher fixed point above four dimensions, using the epsilon expansion.
By computing the lowest operator dimension in the rank-Q symmetric rep in the double-scaling limit where epsilonQ fixed, I will show that its imaginary part never vanishes for any epsilonQ.
The mechanism for the imaginary part is different for small and large...
Defect operators in field theory are very interesting for a number of reasons. Drawing inspiration from techniques which have been very recently applied to uncover interesting properties of sectors of operators with large charge under a global symmetry, we will study simple defects in the Wilson-Fisher fixed point near d=4,6 dimensions. Combining with localization, we will also introduce a...
We study operators with large charge $j$ in the $d$-dimensional $O(N)$ model with long range interactions that decrease with the distance as $1/r^{d+s}$, where $s$ is a continuous parameter. We consider the double scaling limit of large $N$, large $j$ with $j/N=\hat{j}$ fixed, and identify the semiclassical saddle point that captures the two-point function of the large charge operators in this...
