Siavash Golkar

(Non)-renormalization of the chiral vortical effect coefficient

A bstractWe show using diagramtic arguments that in some (but not all) cases, the temperature dependent part of the chiral vortical effect coefficient is independent of the coupling constant. An interpretation of this result in terms of quantization in the effective 3 dimensional Chern-Simons theory is also given. In the language of 3D, dimensionally reduced theory, the value of the chiral vortical coefficient is related to the formula ∑n = 1∞n = − 1/12 . We also show that in the presence of dynamical gauge fields, the CVE coefficient is not protected from renormalization, even in the large N limit.

Global Anomalies and Effective Field Theory

A bstractWe show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory, where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient (up to an overall additive factor). This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.

Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories

A bstractWe explore the consequences of conformal symmetry for the operator product expansions in nonrelativistic field theories. Similar to the relativistic case, the OPE coefficients of descendants are related to that of the primary. However, unlike relativistic CFTs the 3-point function of primaries is not completely specified by conformal symmetry. Here, we show that the 3-point function between operators with nonzero particle number, where (at least) one operator has the lowest dimension allowed by unitarity, is determined up to a numerical coefficient. We also look at the structure of the family tree of primaries with zero particle number and discuss the presence of conservation laws in this sector.

Higher-Spin Theory of the Magnetorotons

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions ν=N/(2N+1) at large N. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are O(N) neutral excitations, each carrying a well-defined spin that runs integer values 2,3,…. The mixing of modes at nonzero momentum q leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at qℓ_{B}=z_{i}/(2N+1), where ℓ_{B} is the magnetic length and z_{i} are the zeros of the Bessel function J_{1}, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.

Effective field theory of relativistic quantum hall systems

A bstractMotivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a term of topological nature, which couples the electromagnetic field with a topologically conserved current of 2 + 1 dimensional relativistic fluid. In contrast to the Chern-Simons term, the new term involves the spacetime metric in a nontrivial way. We extract the predictions of the effective theory for linear electromagnetic and gravitational responses. For fractional quantum Hall states at the zeroth Landau level, additional holomorphic constraints allow one to express the results in terms of two dimensionless constants of topological nature.

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

A bstractWe consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρT(ω) and ρ¯Tω

Hall viscosity, spin density, and torsion

{\overline{\rho}}_T\left(\omega \right)

Particle-hole symmetry and composite fermions in fractional quantum Hall states

, which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S