We 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.

We 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.

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magneto-rotons with dispersion minima at 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 magneto-roton minima. A purely algebraic argument show that the magnetoroton minima are located at q B = zi/(2N + 1), where B is the magnetic length and zi are the zeros of the Bessel function J1, 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. Introduction.-Interacting electrons moving in two dimensions in a strong magnetic field can form nontrivial topological states: the fractional quantum Hall liquids [1, 2]. When the lowest Landau level is filled at certain rational filling fractions, including ν = N/(2N + 1) and ν = (N + 1)/(2N + 1) (the Jain's sequences), the quantum Hall liquid is gapped, and the lowest energy mode is a neutral mode. Girvin, MacDonald, and Platzman [3] proposed, based on a variational ansatz that the neutral excitation has a broad minimum at q B ∼ 1 at the Laughlin plateau ν = 1/3. Several years later, the existence of a neutral mode was confirmed experimentally [4]. Later experiments reveal surprising richness in the structure of the spectrum of neutral excitations. Unexpectedly, the ν = 1/3 state may have more than one branches of excitations [5]. Furthermore, higher in the Jain sequence, i.e., for ν = 2/5, 3/7, etc., the lowest excitation has been found to have a dispersion with more than one minima [6,7]. Various theoretical approaches have been brought to the problem of the magneto-roton [8][9][10][11][12]. Currently, the most common viewpoint is based on the composite fermion picture of the fractional quantum Hall effect, in which the neutral modes are bound states of a composite fermion and a composite hole.The notion of the composite fermion is tightly connected to the Halperin-Lee-Read (HLR) field theory [13], proposed as the low-energy description of the half-filled Landau level. Recently, an analysis of the particle-hole symmetry of the lowest Landau level has lead to a revision of the HLR proposal: the low-energy degrees of freedom is now a Dirac composite fermion coupled to a gauge field [14]. Magneto-rotons provide a rare window into the dynamics of a Fermi surface coupled to a gauge field, a long-standing problem of condensed matter

Abstract:We 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.