Field Theory Interpretation Research Articles

Entropy functional and the holographic attractor mechanism

We provide a field theory interpretation of the attractor mechanism for asymptotically AdS4 dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.

The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator

The [Formula: see text]-adic Kummer–Leopoldt constant [Formula: see text] of a number field [Formula: see text] is (assuming the Leopoldt conjecture) the least integer [Formula: see text] such that for all [Formula: see text], any global unit of [Formula: see text], which is locally a [Formula: see text]th power at the [Formula: see text]-places, is necessarily the [Formula: see text]th power of a global unit of [Formula: see text]. This constant has been computed by Assim and Nguyen Quang Do using Iwasawa’s techniques, after intricate studies and calculations by many authors. We give an elementary [Formula: see text]-adic proof and an improvement of these results, then a class field theory interpretation of [Formula: see text]. We give some applications (including generalizations of Kummer’s lemma on regular [Formula: see text]th cyclotomic fields) and a natural definition of the normalized [Formula: see text]-adic regulator for any [Formula: see text] and any [Formula: see text]. This is done without analytical computations, using only class field theory and especially the properties of the so-called [Formula: see text]-torsion group [Formula: see text] of Abelian [Formula: see text]-ramification theory over [Formula: see text].

On the Ohno–Nakagawa Theorem

In this paper we give a new proof of the Ohno–Nakagawa Theorem using the techniques of L-series. By applying Eisenstein's parametrization of binary cubic forms on the one hand, and a class field theory interpretation of Datskovsky & Wright's Theorem on the other, we reduce the Ohno–Nakagawa Theorem to an identity involving the L-series and the truncated L-series of quadratic orders. We prove this identity by establishing a general relation among these two types L-series.

Mathematical Structure for Electromagnetic Frequencies that May Reflect Pilot Waves of Bohm’s Implicate Order

The mathematical basis for the earlier reported spectrum of discrete electromagnetic field (EMF) frequencies that were shown to affect health and disease is substantiated and generalized in the present paper. The particular EMF pattern was revealed by a meta-analysis of, now, more than 500 biomedical publications that reported life-sustaining as well as life-decaying EMF frequencies. These discrete eigenfrequency values can be related to supposed bio-resonance of solitons or polaron quasi particles in life systems. Bio-solitons are conceived as self-reinforcing solitary waves that are constituting local fields, being involved in intracellular geometric ordering and patterning, as well as in intra- and inter-cellular signalling. Literature search, revealed very similar frequency patterns for wave resonances of nucleotides in aqueous solution, for a candidate RNA-catalyst, as well as for sound-induced vibrations evoked in thin vibrating membranes. This collective evidence points at a generalized biophysical algorithm underlying complexity in nature, evidently manifest in both animate and non-animate modalities. The detected EMF eigenfrequencies could be arithmetically scaled according to an adapted Pythagorean tuning. The mathematical analysis shows that the derived arithmetical scale exhibits a sequence of unique products of integer powers of 2, 3 and a factor . This generalized semi-harmonic frequency spectrum may reflect a discrete pilot-wave structure that can be interpreted as a, so called, hidden variable in Bohm’s causal interpretation of quantum field theory.

Minimal surfaces in AdS C-metric

We shed some light on the field theory interpretation of C-metric by investigating the minimal surfaces which are homologous to the given boundary regions. The accelerating black holes change the asymptotic structure of the space–time. We focus on the geometry features of the minimal surface and study how deep it reaches into the bulk. The regularized area of the minimal surface is not well defined and we introduce a new quantity D(m,θ0), defined as the minimal surface divided by the area of the given boundary region, to study the system.

Avoiding Haag’s Theorem with Parameterized Quantum Field Theory

Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.

Particles, Cutoffs and Inequivalent Representations

We critically review the recent debate between Doreen Fraser and David Wallace on the interpretation of quantum field theory, with the aim of identifying where the core of the disagreement lies. We show that, despite appearances, their conflict does not concern the existence of particles or the occurrence of unitarily inequivalent representations. Instead, the dispute ultimately turns on the very definition of what a quantum field theory is. We further illustrate the fundamental differences between the two approaches by comparing them both to the Bohmian program in quantum field theory.

Abelian Yang–Baxter deformations and TsT transformations

We prove that abelian Yang–Baxter deformations of superstring coset σ models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and fermionic T duality, and naturally lead to a TsT subgroup of the superduality group OSp(db,db|2df). In cases like AdS5×S5, fermionic deformations necessarily lead to complex models. As an illustration of inequivalent deformations, we give all six abelian deformations of AdS3. We comment on the possible dual field theory interpretation of these (super-)TsT models.

Dynamics of N $$ \mathcal{N} $$ = 4 supersymmetric field theories in 2 + 1 dimensions and their gravity dual

In this note we consider ${\cal N}=4$ SYM theories in 2+1 dimensions with gauge group $U(N)\times U(M)$ and $k$ hypermultiplets charged under the $U(N)$. When $k > 2(N-M)$, the theory flows to a superconformal fixed point in the IR. Theories with $k <2(N-M)$, on the other hand, flows to strong coupling. We explore these theories from the perspective of gravity dual. We find that the gravity duals of theories with $k < (N-M)$ contain enhancons even in situations where repulson singularities are absent. We argue that supergravity description is unreliable in the region near these enhancon points. Instead, we show how to construct reliable sugra duals to particular points on the Coulomb branch where the enhancon is screened. We explore how these singularities reappear as one moves around in Coulomb branch and comment on possible field theory interpretation of this phenomenon. In analyzing gauge/gravity duality for these models, we encountered one unexpected surprise, that the condition for the supergravity solution to be reliable and supersymmetric is somewhat weaker than the expectation from field theory. We also discuss similar issues for theories with $k=0$.

Comments on the diphoton excess: critical reappraisal of effective field theory interpretations

We consider the diphoton excess observed by ATLAS and CMS using the most up-to-date data and estimate the preferred enhancement in the production rate between 8 TeV and 13 TeV. Within the framework of effective field theory (EFT), we then show that for both spin-0 and spin-2 Standard Model (SM) gauge-singlet resonances, two of the three processes S to ZZ, S to Z gamma, and S to WW must occur with a non-zero rate. Moreover, we demonstrate that these branching ratios are highly correlated in the EFT. Couplings of S to additional SM states may be constrained and differentiated by comparing the S production rates with and without the vector-boson fusion (VBF) cuts. We find that for a given VBF to inclusive production ratio there is maximum rate of S to gauge bosons, b b-bar, and lighter quark anti-quark pairs. Simultaneous measurements of the width and the VBF ratio may be able to point towards the existence of hidden decays.

New constraint on effective field theories of the QCD flux tube

Effective magnetic $SU(N)$ gauge theory with classical $Z_N$ flux tubes of intrinsic width $\frac{1}{M}$ is an effective field theory of the long distance quark-antiquark interaction in $SU(N)$ Yang-Mills theory. Long wavelength fluctuations of the $Z_N$ vortices of this theory lead to an effective string theory. In this paper we clarify the connection between effective field theory and effective string theory and we propose a new constraint on these vortices. We first examine the impact of string fluctuations on the classical dual superconductor description of confinement. At inter-quark distances $R\sim \frac{1}{M}$ the classical action for a straight flux tube determines the heavy quark potentials. At distances $R \gg \frac{1}{M}$ fluctuations of the flux tube axis $\tilde{x}$ give rise to an effective string theory with an action $S_{eff} (\tilde{x})$, the classical action for a curved flux tube, evaluated in the limit $\frac{1}{M} \rightarrow 0~$. This action is equal to the Nambu-Goto action. These conclusions are independent of the details of the $Z_N$ flux tube. Further, we assume the QCD flux tube satisfies the additional constraint: $$\int_0^\infty r dr \frac{T_{\theta \theta} (r)}{r^2} =0,$$ where $\frac{T_{\theta \theta}(r)}{r^2}$ is the value of the $\theta\theta$ component of the stress tensor at a distance $r$ from the axis of an infinite flux tube. Under this constraint the string tension $\sigma$ equals the force on a quark in the chromoelectric field $\vec{E}$ of an infinite straight flux tube, and the Nambu-Goto action can be represented in terms of the chromodynamic fields of effective magnetic $SU(N)$ gauge theory, yielding a field theory interpretation of effective string theory.

On the reconstruction of Lifshitz spacetimes

We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or "hole-ography"), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of \cite{Headrick:2014eia}. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.

Metrical interpretation of field theories

Metrical interpretation of field theories

A perspective on non-commutative quantum gravity

In this paper, we present some of the concepts underlying a program of non-commutative quantum gravity and recall some of the results. This program includes a novel approach to spectral triple categorification and also a precise connection between Fell bundles and Connes' non-commutative geometry. Motivated by topics in quantization of the non-commutative standard model and introduction of algebraic techniques and concepts into quantum gravity (following for example Crane, Baez and Barrett), we define spectral C*-categories, which are deformed spectral triples in a sense made precise. This definition gives to representations of a C*-category on a small category of Hilbert spaces and bounded linear maps, the interpretation of a topological quantum field theory. The construction passes two mandatory tests: (i) there is a classical limit theorem reproducing a Riemannian spin manifold manifesting Connes' and Schücker's non-commutative counterpart of Einstein's equivalence principle, and (ii) there is consistency with the experimental fermion mass matrix. We also present an algebra invariant taking the form of a partition function arising from a C*-bundle dynamical system in connection with C*-subalgebra theory.

Simplified dark matter top-quark interactions at the LHC

Stringent limits on the interactions between dark matter (DM) and the standard model (SM) can be set by studying how initial-state or final-state particles recoil against missing transverse energy . In this work, we improve, extend and correct LHC constraints on the interactions between DM and top quarks that are mediated by the exchange of spin-0 s-channel resonances. A comparison of the LHC run-1 sensitivity of the two main search channels is presented, which shows that mono-jet searches are typically more restrictive than the searches. We furthermore explore the reach of the 14 TeV LHC. The collider constraints are compared to the restrictions arising from direct and indirect detection as well as the DM relic abundance, and we also reflect on effective field theory (EFT) interpretations of the LHC exclusions.

Compactifications of the Klebanov-Witten CFT and new AdS 3 backgrounds

In this paper we find various new backgrounds in Type IIB, IIA and M-theory with an $AdS_3$-factor. The solutions are smooth and preserve small amounts of SUSY. These new backgrounds are found by application of non-Abelian T-duality (sometimes combined with T-duality) on the supergravity solution dual to the Klebanov-Witten CFT compactified to two dimensions. The field theory aspects encoded by these backgrounds are studied. We give a detailed account of conserved charges, central charges, entanglement entropy and Wilson loops. Further, we present a possible field theory interpretation for our backgrounds.

Towards a field-theory interpretation of bottom-up holography

We investigate recent results for the electrical conductivity and the fermionic self-energy, obtained in a holographic bottom-up model for a relativistic charge-neutral conformal field theory. We present two possible field-theoretic derivations of these results, using either a semiholographic or a holographic point of view. In the semiholographic interpretation, we also show how, in general, the conductivity should be calculated in agreement with Ward identities. The resulting field-theory interpretation may lead to a better understanding of the holographic dictionary in applied AdS/CMT.

Effective field theory interpretation of searches for dark matter annihilation in the Sun with the IceCube Neutrino Observatory

We present a model-independent interpretation of searches for dark matter annihilation in the Sun using an effective field theory approach. We identify a set of effective operators contributing to spin-dependent scattering of dark matter with protons in the non-relativistic limit and explore simple new physics models which would give rise to such operators. Using the limits on the spin-dependent scattering cross-section set by the IceCube collaboration in their search for dark matter annihilation in the Sun, we derive limits on effective couplings and corresponding masses of mediating particles. We show that the effective field theory interpretation of the IceCube searches provides constraints on dark matter complementary to those from relic density observations and searches at the LHC. Finally, we discuss the impact of astrophysical uncertainties on our results.

Spectral dimensions from the spectral action

The generalized spectral dimension ${D}_{S}(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analyzing the propagation of spin-0, spin-1 and spin-2 fields, we show that a nontrivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateau structures interpolating between a fixed spin-independent ${D}_{S}(T)={d}_{S}$ for short and ${D}_{S}(T)=4$ for long diffusion times $T$. Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding ${D}_{S}(T)=0$ for all spins. Our results support earlier claims that high-energy bosons do not propagate.

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.