Field Theory Interpretation Research Articles

Ginzburg-Landau Approach to Holographic Superconductivity

We construct a family of minimal phenomenological models for holographic superconductors in d=4+1 AdS spacetime and study the effect of scalar and gauge field fluctuations. By making a Ginzburg-Landau interpretation of the dual field theory, we determine through holographic techniques a phenomenological Ginzburg-Landau Lagrangian and the temperature dependence of physical quantities in the superconducting phase. We obtain insight on the behaviour of the Ginzburg-Landau parameter and whether the systems behaves as a Type I or Type II superconductor. Finally, we apply a constant external magnetic field in a perturbative approach following previous work by D'Hoker and Kraus, and obtain droplet solutions which signal the appearance of the Meissner effect.

The Shaky Game +25, or: on locavoracity

Taking Arthur Fine’s The Shaky Game as my inspiration, and the recent 25\({\textit{th}}\) anniversary of the publication of that work as the occasion to exercise that inspiration, I sketch an alternative to the “Naturalism” prevalent among philosophers of physics. Naturalism is a methodology eventuating in a metaphysics. The methodology is to seek the deep framework assumptions that make the best sense of science; the metaphysics is furnished by those assumptions and supported by their own support of science. The alternative presented here, which I call “Locavoracity,” shares Naturalism’s commitment to making sense of science, but alters Naturalism’s methodology. The Locavore’s sense-making projects are piecemeal, rather than sweeping. The Locavore’s hypothesis is that the collection of local sense-making projects fails to issue a single overarching unifying framework deserving of the title “the metaphysics that makes the best sense of science.” I muster some examples supporting the Locavore hypothesis from the interpretation of quantum field theories.

Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization

We study determinantal random point processes on a compact complex manifold X associated to a Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a gas of free fermions on X subject to a U(1)-gauge field and when X is the Riemann sphere it specializes to various random matrix ensembles. Our general setup will also include the setting of weighted orthogonal polynomials in $${\mathbb{C}^{n}}$$ , as well as in $${\mathbb{R}^{n}}$$ . It is shown that, in the many particle limit, the empirical random measures on X converge exponentially towards the deterministic pluripotential equilibrium measure, defined in terms of the Monge–Ampère operator of complex pluripotential theory. More precisely, a large deviation principle (LDP) is established with a good rate functional which coincides with the (normalized) pluricomplex energy of a measure recently introduced in Berman et al. (Publ Math de l’IHÉS 117, 179–245, 2013). We also express the LDP in terms of the Ray–Singer analytic torsion. This can be seen as an effective bosonization formula, generalizing the previously known formula in the Riemann surface case to higher dimensions and the paper is concluded with a heuristic quantum field theory interpretation of the resulting effective boson–fermion correspondence.

Beyond effective field theory for dark matter searches at the LHC

We study the validity of effective field theory (EFT) interpretations of monojet searches for dark matter at the LHC for vector and axial-vector interactions. We show that the EFT approach is valid when the mediator has mass m med greater than 2.5 TeV. We find that the current limits on the contact interaction scale Λ in the EFT apply to theories that are perturbative for dark matter mass m DM < 800 GeV. However, for all values of m DM in these theories, the mediator width is larger than the mass, so that a particle-like interpretation of the mediator is doubtful. Furthermore, consistency with the thermal relic density occurs only for 170 ≲ m DM ≲ 510 GeV. For lighter mediator masses, the EFT limit either under-estimates the true limit (because the process is resonantly enhanced) or over-estimates it (because the missing energy distribution is too soft). We give some ‘rules of thumb’ that can be used to estimate the limit on Λ (to an accuracy of ~ 50 %) for any m DM and m med from knowledge of the EFT limit. We also compare the relative sensitivities of monojet and dark matter direct detection searches finding that both dominate in different regions of the m DM - m med plane. Comparing only the EFT limit with direct searches is misleading and can lead to incorrect conclusions about the relative sensitivity of the two search approaches.

Trope ontology and algebraic quantum field theory: An Evaluation of Kuhlmann's proposal

Meinard Kuhlmann has recently provided an interpretation of quantum field theory that seems to offer an alternative to the particle and field interpretations. The main idea is to adopt a trope ontology and, then, consider particles and fields as derivative entities. The aim of this paper is to discuss Kuhlmann's proposal. In the first part of the paper I will offer a reconstruction of his position. I will then show that this interpretation faces some problems about the distinction between essential and non-essential tropes and their link to the formalism of algebraic quantum field theory, which is the formulation of the theory that Kuhlmann adopts in his interpretation. Finally, I will show how Kuhlmann's proposal might share some problems with the particle and field interpretations, namely the localization problem and the Unruh effect.

Effective field theory in time-dependent settings

We use the in-in or Schwinger-Keldysh formalism to explore the construction and interpretation of effective field theories for time-dependent systems evolving out of equilibrium. Starting with a simple model consisting of a heavy and a light scalar field taken to be in their free vacuum states at a finite initial time, we study the effects from the heavy field on the dynamics of the light field by analyzing the equation of motion for the expectation value of the light background field. New terms appear which cannot arise from a local action of an effective field theory in terms of the light field, though they disappear in the adiabatic limit. We discuss the origins of these terms as well as their possible implications for time dependent situations such as inflation.

On field theory thermalization from gravitational collapse

Motivated by its field theory interpretation, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. After demonstrating the accuracy of the numerical algorithm for the questions we are interested in, we investigate various aspects of the apparent horizon formation. In particular, we study the time and radius of the apparent horizon formed as functions of the initial Gaussian profile for the scalar field. We comment on several aspects of the dual field theory picture.

Generalized [formula omitted] topological amplitudes and holomorphic anomaly equation

In arXiv:0905.3629 we described a new class of N = 2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which appear at higher loops in heterotic string theory compactified on K 3 × T 2 . We analyze their effective field theory interpretation and derive particular (first order) differential equations as a consequence of supersymmetry Ward identities and the 1/2-BPS nature of the corresponding effective action terms. In string theory the latter get modified due to anomalous world-sheet boundary contributions, generalizing in a non-trivial way the familiar holomorphic and harmonicity anomalies studied in the past. We prove by direct computation that the subclass of topological amplitudes studied in arXiv:0905.3629 forms a closed set under these anomaly equations and that these equations are integrable.

Gravitational and Yang-Mills instantons in holographic RG flows

We study various holographic RG flow solutions involving warped asymptotically locally Euclidean (ALE) spaces of $A_{N-1}$ type. A two-dimensional RG flow from a UV (2,0) CFT to a (4,0) CFT in the IR is found in the context of (1,0) six dimensional supergravity, interpolating between $AdS_3\times S^3/\mathbb{Z}_N$ and $AdS_3\times S^3$ geometries. We also find solutions involving non trivial gauge fields in the form of SU(2) Yang-Mills instantons on ALE spaces. Both flows are of vev type, driven by a vacuum expectation value of a marginal operator. RG flows in four dimensional field theories are studied in the type IIB and type I$'$ context. In type IIB theory, the flow interpolates between $AdS_5\times S^5/\mathbb{Z}_N$ and $AdS_5\times S^5$ geometries. The field theory interpretation is that of an N=2 $SU(n)^N$ quiver gauge theory flowing to N=4 SU(n) gauge theory. In type I$'$ theory the solution describes an RG flow from N=2 quiver gauge theory with a product gauge group to N=2 gauge theory in the IR, with gauge group $USp(n)$. The corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/\mathbb{Z}_2$, respectively. We also explore more general RG flows, in which both the UV and IR CFTs are N=2 quiver gauge theories and the corresponding geometries are $AdS_5\times S^5/(\mathbb{Z}_N\times \mathbb{Z}_2)$ and $AdS_5\times S^5/(\mathbb{Z}_M\times \mathbb{Z}_2)$. Finally, we discuss the matching between the geometric and field theoretic pictures of the flows.

Towards multi-scale dynamics on the baryonic branch of Klebanov-Strassler

We construct explicitly a new class of backgrounds in type-IIB supergravity which generalize the baryonic branch of Klebanov-Strassler. We apply a solution-generating technique that, starting from a large class of solutions of the wrapped-D5 system, yields the new solutions, and then proceed to study in detail their properties, both in the IR and in the UV. We propose a simple intuitive field theory interpretation of the rotation procedure and of the meaning of our new solutions within the Papadopoulos-Tseytlin ansatz, in particular in relation to the duality cascade in the Klebanov-Strassler solution. The presence in the field theory of different VEVs for operators of dimensions 2, 3 and 6 suggests that this is an important step towards the construction of the string dual of a genuinely multi-scale (strongly coupled) dynamical model.

Ideles in Higher Dimension

We propose a notion of idele class groups of finitely generated fields using the concept of Parshin chains. This new class group allows us to give an idelic interpretation of the higher class field theory of Kato and Saito.

From Archimedean L-Factors to Topological Field Theories

We give a short account of our recent results on establishing a relation between topological field theories and Archimedean (∞-adic) geometry. First, we introduce a universal integral Baxter operator as a certain element of the spherical Hecke algebra \({\fancyscript{H}(G,K)}\). Eigenvalues of the Baxter operator acting on spherical vectors in irreducible representations G are given by corresponding local Archimedean L-factors. We provide a quantum field theory interpretation of the local Archimedean L-factors as certain correlation functions in a two-dimensional type A equivariant topological linear sigma model on a disk D. Next, we introduce a q-version of the Archimedean L-factors and construct a particular representation of q-deformed Whittaker functions generalizing the Casselman–Shalika formula for p-adic class one Whittaker functions. This representation allows to formulate a q-version of Archimedean Langlands correspondence. Then, we construct a representation of q-version of the Archimedean L-factors as a certain correlation functions in three-dimensional equivariant linear sigma model on D × S1. Finally, we propose an interpretation of the Archimedean Langlands correspondence as a mirror symmetry in the underlying topological quantum field theory.

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.

Effects of interactions on the topological classification of free fermion systems

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification is an integer, but with the introduction of interactions it becomes well defined only modulo 8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct free phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field theory interpretation of this phenomenon. There is a second order phase transition between the two phases in the free theory which can be avoided by going through the strongly interacting region. We show that this transition is in the 2D Ising universality class, where a first order phase transition line, terminating at a second order transition, can be avoided by going through the analogue of a high temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e. the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first order Peierls transition region, a second order transition region, and a region with no transition.

Universal time-dependent deformations of Schrödinger geometry

We investigate universal time-dependent exact deformations of Schrodinger geometry. We present 1) scale invariant but non-conformal deformation, 2) non-conformal but scale invariant deformation, and 3) both scale and conformal invariant deformation. All these solutions are universal in the sense that we could embed them in any supergravity constructions of the Schrodinger invariant geometry. We give a field theory interpretation of our time-dependent solutions. In particular, we argue that any time-dependent chemical potential can be treated exactly in our gravity dual approach.

Stringy instantons from Seiberg duality

AbstractWe review the field theory interpretation in terms of Seiberg duality of the non perturbative contribution due to a SU(1) stringy instanton.

N=2cascade revisited and the enhançon bearings

Supergravity backgrounds with varying fluxes generated by fractional branes at nonisolated Calabi-Yau singularities had escaped a precise dual field theory interpretation so far. In the present work, considering the prototypical example of such models, the $\mathbb{C}\ifmmode\times\else\texttimes\fi{}{\mathbb{C}}^{2}/{\mathbb{Z}}_{2}$ orbifold, we propose a solution for this problem, and show that the known cascading solution corresponds to a vacuum on the Coulomb branch of the corresponding quiver gauge theory involving a sequence of strong coupling transitions reminiscent of the baryonic root of $\mathcal{N}=2$ supersymmetric quantum chromodynamics . We also find a slight modification of this cascading vacuum which upon mass deformation is expected to flow to the Klebanov-Strassler cascade. Finally, we discuss an infinite class of vacua on the Coulomb branch whose renormalization group flows include infinitely coupled conformal regimes, and explain their gravitational manifestation in terms of new geometric structures that we dub enhan\ifmmode \mbox{\c{c}}\else \c{c}\fi{}on bearings. Repulson-free backgrounds dual to all the vacua we analyze are explicitly provided.

An Interpretation of Algebraic Quantum Field Theory from a Semirealistic Point of View(Issues in the Philosophy of Quantum Mechanics (1))

An Interpretation of Algebraic Quantum Field Theory from a Semirealistic Point of View(Issues in the Philosophy of Quantum Mechanics (1))

Scattering of single spikes

We apply the dressing method to a string solution given by a static string wrapped around the equator of a three-sphere and find that the result is the single spike solution recently discussed in the literature. Further application of the method allows the construction of solutions with multiple spikes. In particular we construct the solution describing the scattering of two single spikes and compute the scattering phase shift. As a function of the dressing parameters, the result is exactly the same as the one for the giant magnon, up to non-logarithmic terms. This suggests that the single spikes should be described by an integrable spin chain closely related to the one associated to the giant magnons. The field theory interpretation of such spin chain however is still unclear.

Radion phenomenology in realistic warped space models

We investigate the phenomenology of the Randall-Sundrum (RS) radion in realistic models of electroweak symmetry breaking with bulk gauge and fermion fields, since the radion may turn out to be the lightest particle in such models. We calculate the coupling of the radion in such scenarios to bulk fermion and gauge modes. Special attention needs to be devoted to the coupling to massless gauge fields (photon, gluon), since it is well known that loop effects may be important for these fields. We also present a detailed explanation of these couplings from the conformal field theory interpretation. We then use these couplings to determine the radion branching fractions and discuss some of the discovery potential of the LHC for the radion. We find that the $\ensuremath{\gamma}\ensuremath{\gamma}$ signal is enhanced over most of the range of the radion mass over the $\ensuremath{\gamma}\ensuremath{\gamma}$ signal of a standard model Higgs boson, as long as the RS scale is sufficiently low. However, the signal significance depends strongly on free parameters that characterize the magnitude of bare brane-localized kinetic terms for the massless gauge fields. In the absence of such terms, the signal can be enhanced over the traditional RS1 models (where all standard model fields are localized on the IR brane), but the signal can also be reduced compared to RS1 if the brane-localized terms are sizeable. We also show that for larger radion masses, where the $\ensuremath{\gamma}\ensuremath{\gamma}$ signal is no longer significant, one can use the usual 4 lepton signal to discover the radion.