Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

We compute the 1-loop partition function for strings in $AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.Comment: 28 page

Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions

We find 1/6 BPS string configurations in AdS_4 x CP^3, which we identify as the duals of certain 1/6 BPS circular Wilson loops in N=6 super Chern-Simons-matter gauge theory. We use our results to verify -in the strong coupling limit- a proposal made in arXiv:1402.4128 for a relation between the expectation value of these Wilson loops and the Bremsstrahlung function from deforming 1/2 BPS Wilson lines with a cusp. We also derive an analogous relation between the expectation value of some particular 1/12 BPS Wilson loops and the Bremsstrahlung function from deforming 1/6 BPS Wilson lines with an internal space cusp.Comment: 25 pages, 1 figures; v2 author ordering correcte

Circular Wilson loops in defect conformal field theory

We study a D3-D5 system dual to a conformal field theory with a codimension-one defect that separates regions where the ranks of the gauge groups differ by k. With the help of this additional parameter, as observed by Nagasaki, Tanida and Yamaguchi, one can define a double scaling limit in which the quantum corrections are organized in powers of λ/k2, which should allow to extrapolate results between weak and strong coupling regimes. In particular we consider a radius R circular Wilson loop placed at a distance L, whose internal space orientation is given by an angle χ. We compute its vacuum expectation value and show that, in the double scaling limit and for small χ and small L/R, weak coupling results can be extrapolated to the strong coupling limit.Fil: Aguilera Damia, Jeremías. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Correa, Diego Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Giraldo Rivera, Victor Ivan. International Centre For Theoretical Sciences; India. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Nonrelativistic Dirac fermions on the torus

Two dimensional conformal feld theories have been extensively studied in the past. When considered on the torus, they are strongly constrained by modular invariance. However, introducing relevant deformations or chemical potentials pushes these theories away from criticality, where many of their aspects are still poorly understood. In this note we make a step towards filling this gap, by analyzing the theory of a Dirac fermion on the torus, deformed by a mass term and a chemical potential for the particle number symmetry. The theory breaks conformal and Lorentz invariance, and we study its spectrum and partition function. We also focus on two limits that are interesting on their own right: a massless relativistic fermion with nonzero chemical potential (a simple model for CFTs at finite density), and nonrelativistic Schrodinger fermions (of relevance in condensed matter systems). Taking inspiration from recent developments in massive modular forms, we obtain a representation of the torus free energy based on Fourier-transforming over a twisted boundary condition. This dual representation fullfills many properties analogous to modular invariance in CFTs. In particular, we use this result to derive Cardy-like formulas for the high energy density of states of these theories.Comment: 23 pages, v2 reference adde

When the moduli space is an orbifold: Spontaneous breaking of continuous non-invertible symmetries

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space.Comment: 21 page

Non-Invertible Defects in 5d, Boundaries and Holography

We show that very simple theories of abelian gauge fields with a cubic Chern-Simons term in 5d have an infinite number of non-invertible co-dimension two defects. They arise by dressing the symmetry operators of the broken electric 1-form symmetry with a suitable topological field theory, for any rational angle. We further discuss the same theories in the presence of a 4d boundary, and more particularly in a holographic setting. There we find that the bulk defects, when pushed to the boundary, have various different fates. Most notably, they can become co-dimension one non-invertible defects of a boundary theory with an ABJ anomaly.Comment: v3: Journal Versio

How non-Fermi liquids cure their infrared divergences

Non-Fermi liquids in d=2 spatial dimensions can arise from coupling a Fermi surface to a gapless boson. At finite temperature, however, the perturbative quantum field theory description breaks down due to infrared divergences. These are caused by virtual static bosonic modes and affect both fermionic and bosonic correlators. We show how these divergences are resolved by self-consistent boson and fermion self-energies that resum an infinite class of diagrams and correct the standard Eliashberg equations. Extending a previous approach in d=3-ϵ dimensions, we find a new "thermal non-Fermi liquid"regime that violates the scaling laws of the zero-temperature fixed point and dominates over a wide range of scales. We conclude that basic properties of quantum phase transitions and quantum-classical crossovers at finite temperature are modified in crucial ways in systems with soft bosonic fluctuations, and we begin a study of some of the phenomenological consequences.Fil: Aguilera Damia, Jeremías. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Solís Delgadillo, Juan Mario. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Torroba, Gonzalo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

We compute the 1-loop partition function for strings in AdS4 × ℂℙ3, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.Instituto de Física La Plat

Two-Dimensional Non-Fermi-Liquid Metals: A Solvable Large-N Limit

Significant effort has been devoted to the study of “non-Fermi-liquid” (NFL) metals: gapless conducting systems that lack a quasiparticle description. One class of NFL metals involves a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point. The problem has been extensively studied in a large-N limit (N corresponding to the number of fermion flavors) where universal behavior can be obtained by solving a set of coupled saddle-point equations. However, a remarkable study by Lee revealed the breakdown of such approximations in two spatial dimensions. We show that an alternate approach, in which the fermions belong to the fundamental representation of a global SUðNÞ flavor symmetry, while the order parameter fields transform under the adjoint representation (a “matrix large-N” theory), yields a tractable large N limit. At low energies, the system consists of an overdamped boson with dynamical exponent z ¼ 3 coupled to a non-Fermi-liquid with self-energy ΣðωÞ ∼ ω2=3 , consistent with previous studies.Fil: Aguilera Damia, Jeremías. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kachru, Shamit. University of Stanford; Estados UnidosFil: Raghu, Srinivas. Slac National Accelerator Laboratory; Estados Unidos. University of Stanford; Estados UnidosFil: Torroba, Gonzalo. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin