1,721,001 research outputs found
Conformal Dimensions in the Large Charge Sectors at the O (4) Wilson-Fisher Fixed Point
Full text linkWe study the Oð4Þ Wilson-Fisher fixed point in 2 + 1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (jL; jR). Using effective field theory we derive a formula for the conformal dimensions D(jL; jR) of the leading operator in terms of two constants, c3=2 and c1=2, when the sum jL þ jR is much larger than the difference jL − jR . We compute D(jL ; jR) when jL = jR with Monte Carlo calculations in a discrete formulation of the Oð4Þ lattice field theory, and show excellent agreement with the predicted formula and estimate c3=2 = 1.068(4) and c1/2 = 0.083(3)
Following the flow for large N and large charge
Full text linkWe discuss the 0(2N) vector model in three dimensions. While this model flows to the Wilson–Fisher fixed point when fine tuned, working in a double-scaling limit of large N and large charge allows us to study the model away from the critical point and even to follow the RG flow from the UV to the IR. The crucial observation is that the effective potential — at leading order in N but exact to all orders in perturbation theory — is the Legendre transform of the grand potential at fixed charge. This allows us to write an effective action and the free energy for generic values of the coupling in a very simple fashion and without evaluating any Feynman diagrams
Large charge at large N
Full text linkWe apply the large-charge expansion to O(N) vector models starting from first principles, focusing on the Wilson-Fisher point in three dimensions. We compute conformal dimensions at zero and finite temperature at fixed charge Q, concentrating on the regime 1 « N « Q. Our approach places the earlier effective field theory treatment on firm ground and extends its predictions.We apply the large-charge expansion to O(N) vector models starting from first principles, focusing on the Wilson-Fisher point in three dimensions. We compute conformal dimensions at zero and finite temperature at fixed charge Q, concentrating on the regime . Our approach places the earlier effective field theory treatment on firm ground and extends its predictions
Near-Schrödinger dynamics at large charge
Full text linkIn this paper we discuss a nonrelativistic system at large charge in a regime where Schrödinger symmetry is slightly broken by an explicit mass term for the dilaton field which nonlinearly realizes nonrelativistic scale invariance. To get there, we first develop the large-charge formalism from the linear sigma model perspective, including the harmonic trapping potential necessary for the nonrelativistic state-operator correspondence. As a signature of the explicit breaking, we identify a √QlogQ term, which depending on the space dimension is either of the same order as the effects coming from the breakdown of the EFT at the edge of the particle cloud, or can be distinguished from these effects over a large range of orders of magnitude
Quantum crystals, Kagome lattice, and plane partitions fermion-boson duality
Full text linkIn this work we study quantum crystal melting in three space dimensions. Using an equivalent description in terms of dimers in a hexagonal lattice, we recast the crystal melting Hamiltonian as an occupancy problem in a Kagome lattice. The Hilbert space is spanned by states labeled by plane partitions, and, writing them as a product of interlaced integer partitions, we define a fermion-boson duality for plane
partitions. Finally, based upon the latter result we conjecture that the growth operators for the quantum Hamiltonian can be represented in terms of the affine Yangian Y[gl(1)]
Convexity, large charge and the large-N phase diagram of the φ4 theory
Full text linkIn this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2 < D < 4 and 4 < D < 6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2 < D < 4, the theory is well-behaved, the model in 4 < D < 6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder
Line operators from M-branes on compact Riemann surfaces
Full text linkIn this paper, we determine the charge lattice of mutually local Wilson and ’t Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. The latterplays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Resurgence of the large-charge expansion
Full text linkWe study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data
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