The (2 + 1)-d U (1) quantum link model masquerading as deconfined criticality

The (2 + 1)-d U(1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a (2 + 1)-d RP(1) effective field theory, perturbed by an SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma

The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed.

An estimate of heavy quark momentum diffusion coefficient in gluon plasma

We calculate the momentum diffusion coefficient for heavy quarks in SU(3) gluon plasma at temperatures 1-2 times the deconfinement temperature. The momentum diffusion coefficient is extracted from a Monte Carlo calculation of the correlation function of color electric fields, in the leading order of expansion in heavy quark mass. Systematics of the calculation are examined, and compared with perturbtion theory and other estimates.

Kubo relations and radiative corrections for lepton number washout

The rates for lepton number washout in extensions of the Standard Model containing right-handed neutrinos are key ingredients in scenarios for baryogenesis through leptogenesis. We relate these rates to real-time correlation functions at finite temperature, without making use of any particle approximations. The relations are valid to quadratic order in neutrino Yukawa couplings and to all orders in Standard Model couplings. They take into account all spectator processes, and apply both in the symmetric and in the Higgs phase of the electroweak theory. We use the relations to compute washout rates at next-to-leading order in g, where g denotes a Standard Model gauge or Yukawa coupling, both in the non-relativistic and in the relativistic regime. Even in the non-relativistic regime the parametrically dominant radiative corrections are only suppressed by a single power of g. In the non-relativistic regime radiative corrections increase the washout rate by a few percent at high temperatures, but they are of order unity around the weak scale and in the relativistic regime.

Black probes of Schrödinger spacetimes

We consider black probes of Anti-de Sitter and Schrödinger spacetimes embedded in string theory and M-theory and construct perturbatively new black hole geometries. We begin by reviewing black string configurations in Anti-de Sitter dual to finite temperature Wilson loops in the deconfined phase of the gauge theory and generalise the construction to the confined phase. We then consider black strings in thermal Schrödinger, obtained via a null Melvin twist of the extremal D3-brane, and construct three distinct types of black string configurations with spacelike as well as lightlike separated boundary endpoints. One of these configurations interpolates between the Wilson loop operators, with bulk duals defined in Anti-de Sitter and another class of Wilson loop operators, with bulk duals defined in Schrödinger. The case of black membranes with boundary endpoints on the M5-brane dual to Wilson surfaces in the gauge theory is analysed in detail. Four types of black membranes, ending on the null Melvin twist of the extremal M5-brane exhibiting the Schrödinger symmetry group, are then constructed. We highlight the differences between Anti-de Sitter and Schrödinger backgrounds and make some comments on the properties of the corresponding dual gauge theories.

Standard Model thermodynamics across the electroweak crossover

Even though the Standard Model with a Higgs mass mH = 125GeV possesses no bulk phase transition, its thermodynamics still experiences a "soft point" at temperatures around T = 160GeV, with a deviation from ideal gas thermodynamics. Such a deviation may have an effect on precision computations of weakly interacting dark matter relic abundances if their mass is in the few TeV range, or on leptogenesis scenarios operating in this temperature range. By making use of results from lattice simulations based on a dimensionally reduced effective field theory, we estimate the relevant thermodynamic functions across the crossover. The results are tabulated in a numerical form permitting for their insertion as a background equation of state into cosmological particle production/decoupling codes. We find that Higgs dynamics induces a non-trivial "structure" visible e.g. in the heat capacity, but that in general the largest radiative corrections originate from QCD effects, reducing the energy density by a couple of percent from the free value even at T > 160GeV.

The braneology of 3D dualities

In this paper, we study the reduction of four-dimensional Seiberg duality to three dimensions from a brane perspective. We reproduce the nonperturbative dynamics of three-dimensional field theory via a T–duality at a finite radius and the action of Euclidean D–strings. In this way, we also overcome certain issues regarding the brane description of Aharony duality. Moreover, we apply our strategy to more general dualities, such as toric duality for M2–branes and dualities with adjoint matter fields.

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

A gauge theory for continuous spin particles

In this dissertation we explore the features of a Gauge Field Theory formulation for continuous spin particles (CSP). To make our discussion as self-contained as possible, we begin by introducing all the basics of Group Theory - and representation theory - which are necessary to understand where the CSP come from. We then apply what we learn from Group Theory to the study of the Lorentz and Poincaré groups, to the point where we are able to construct the CSP representation. Finally, after a brief review of the Higher-Spin formalism, through the Schwinger-Fronsdal actions, we enter the realm of CSP Field Theory. We study and explore all the local symmetries of the CSP action, as well as all of the nuances associated with the introduction of an enlarged spacetime, which is used to formulate the CSP action. We end our discussion by showing that the physical contents of the CSP action are precisely what we expected them to be, in comparison to our Group Theoretical approach.

Transport across two interacting quantum dots: Bulk Kondo, Kondo box, and molecular regimes

We analyze the transport properties of a double quantum dot device with both dots coupled to perfect conducting leads and to a finite chain of N noninteracting sites connecting both of them. The interdot chain strongly influences the transport across the system and the local density of states of the dots. We study the case of a small number of sites, so that Kondo box effects are present, varying the coupling between the dots and the chain. For odd N and small coupling between the interdot chain and the dots, a state with two coexisting Kondo regimes develops: the bulk Kondo due to the quantum dots connected to leads and the one produced by the screening of the quantum dot spins by the spin in the finite chain at the Fermi level. As the coupling to the interdot chain increases, there is a crossover to a molecular Kondo effect, due to the screening of the molecule (formed by the finite chain and the quantum dots) spin by the leads. For even N the two Kondo temperatures regime does not develop and the physics is dominated by the usual competition between Kondo and antiferromagnetism between the quantum dots. We finally study how the transport properties are affected as N is increased. For the study we used exact multiconfigurational Lanczos calculations and finite-U slave-boson mean-field theory at T=0. The results obtained with both methods describe qualitatively and also quantitatively the same physics.

Temperature measured in permafrost borehole at ICDP site 5011-3 in El'gygytgyn Crater, 2008-2011

This study focuses on the temperature field observed in boreholes drilled as part of interdisciplinary scientific campaign targeting the El'gygytgyn Crater Lake in NE Russia. Temperature data are available from two sites: the lake borehole 5011-1 located near the center of the lake reaching 400 m depth, and the land borehole 5011-3 at the rim of the lake, with a depth of 140 m. Constraints on permafrost depth and past climate changes are derived from numerical simulation of the thermal regime associated with the lake-related talik structure. The thermal properties of the subsurface needed for these simulations are based on laboratory measurements of representative cores from the quaternary sediments and the underlying impact-affected rock, complemented by further information from geophysical logs and data from published literature. The temperature observations in the lake borehole 5011-1 are dominated by thermal perturbations related to the drilling process, and thus only give reliable values for the lowermost value in the borehole. Undisturbed temperature data recorded over more than two years are available in the 140 m deep land-based borehole 5011-3. The analysis of these observations allows determination of not only the recent mean annual ground surface temperature, but also the ground surface temperature history, though with large uncertainties. Although the depth of this borehole is by far too insufficient for a complete reconstruction of past temperatures back to the Last Glacial Maximum, it still affects the thermal regime, and thus permafrost depth. This effect is constrained by numerical modeling: assuming that the lake borehole observations are hardly influenced by the past changes in surface air temperature, an estimate of steady-state conditions is possible, leading to a meaningful value of 14 ± 5 K for the post-glacial warming. The strong curvature of the temperature data in shallower depths around 60 m can be explained by a comparatively large amplitude of the Little Ice Age (up to 4 K), with low temperatures prevailing far into the 20th century. Other mechanisms, like varying porosity, may also have an influence on the temperature profile, however, our modeling studies imply a major contribution from recent climate changes.

Indications of coherence-incoherence crossover in layered metallic transport

For many strongly correlated metals with layered crystal structure the temperature dependence of the interlayer resistance is different to that of the intralayer resistance. We consider a small polaron model which exhibits this behavior, illustrating how the interlayer transport is related to the coherence of quasiparticles within the layers. Explicit results are also given for the electron spectral function, interlayer optical conductivity, and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and the other incoherent (dominant at high temperatures).

Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Neel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.