Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes

Física Teórica, Atómica y Óptic

Higgs phase in a gauge U(1)\mathbf{U}(1) non-linear CP1\mathbf{CP}^1-model. Two species of BPS vortices and their zero modes

In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.Comment: 17 pages, 28 figure

Modern Approaches to Non-Perturbative QCD and other Confining Gauge Theories

This book contains seven reviews and four research articles on the various modern approaches to the problem of quark confinement in quantum chromodynamics (QCD). These approaches include microscopic models of the Yang–Mills vacuum, which are based on the condensation of magnetic monopoles and center vortices, as well as the models of the confining quark-antiquark string. Possible applications of these models to the analysis of the novel superinsulating state, which emerges in such condensed-matter systems as Josephson junction arrays, are further discussed in one of the reviews. Two reviews from this collection discuss the approaches towards the analytic construction of effective confining theories, at the classical level and within the center-vortex model of the Yang–Mills vacuum. Other aspects of non-perturbative physics addressed by this collection include a possible connection between the localization of low-lying Dirac eigenmodes with the deconfinement and the chiral QCD phase transitions, as well as the role of topology in baryon-rich matter. Last but not least, a novel model of dark matter, based on ultralight axion particles, whose masses are arising due to distinct SU(2) Yang–Mills scales and the Planck mass, is suggested and developed in one of the contributed articles

Space(time) oddity: dualities, holography and branes

In this Thesis, we study (several) aspects of three and five dimensional non-supersymmetric gauge theories. Using non-perturbative techniques, such as known strong-weak coupling dualities and holography, we present new results concerning their dynamics and phase diagrams. The thesis is divided into six Chapters. In the first Chapter, we start reviewing some general aspects of non-supersymmetric three dimensional theories, focusing on the dynamics of gauge theory both in the absence and in presence of Chern-Simons terms. We then focus on known dualities among three dimensional theories, such as particle-vortex and bosonization duality. Thanks to these tools, we discuss what is known about the phase diagram of QCD3, namely the three dimensional analog of four dimensional quantum chromodynamics, for various ranges of its parameters. In Chapter two, we introduce the basics of holography, starting by reviewing the AdS/CFT correspondence. We then generalize the discussion to the case of non-conformal field theories, with particular emphasis on the description of confining theories. Finally, we review the holographic construction of four dimensional and three dimensional gauge theories, and, focusing on the latter case, we construct the gravity dual of QCD3. In Chapter three, we show new results regarding the phase diagram of QCD3 in presence of flavor-breaking mass deformation. The corresponding theory, namely QCD3 with two sets of flavors, is studied in detail, thanks to the conjectured infrared dualities characterizing gauge theories with matter in three dimensions, namely boson-fermion dualities. In particular, the low-energy phase diagram is charted, and its consistency gives additional support to the conjectured phase diagram of QCD3. Moreover, new non-perturbative phases are observed, together with peculiar phase transitions among them, which are novel to QCD3 with two flavors. In Chapter four, we study the phase diagram of large N QCD3 through its holographic dual. This novel study shows perfect agreement with the field theory analysis, giving a simple explanation of the observed peculiarity of its phase diagram, together with an holographic evidence of the validity of boson-fermion dualities. In Chapter five, we review the main aspects of five dimensional theories. Firstly, we focus on general properties of supersymmetric gauge theories, their BPS spectrum, and their moduli spaces of vacua. Then, we study their non-perturbative dynamics using string constructions, both in type I’ and in type IIB string theory. The latter type of construction, known as the pq-web or brane web construction, gives us the possibility of studying in detail many non-perturbative phenomena characterizing these theories and their superconformal ultraviolet fixed points, such as global symmetry enhancement and continuation past infinite coupling

BPS Approaches to Anyons, Quantum Hall States and Quantum Gravity

We study three types of theories, using supersymmetry and ideas from string theory as tools to gain understanding of systems of more general interest. Firstly, we introduce non-relativistic Chern-Simons-matter field theories in three dimensions and study their anyonic spectrum in a conformal phase. These theories have supersymmetric completions, which in the non-relativistic case suffices to protect certain would-be BPS quantities from corrections. This allows us to compute one-loop exact anomalous dimensions of various bound states of non-Abelian anyons, analyse some interesting unitarity bound violations, and test some recently proposed bosonization dualities. Secondly, we turn on a chemical potential and break conformal invariance, putting the theory into the regime of the Fractional Quantum Hall Effect (FQHE). This is illustrated in detail: the theory supports would-be BPS vortices which model the electrons of the FQHE, and they form bag-like states with the appropriate filling fractions, Hall conductivities, and anyonic excitations. This formalism makes possible some novel explicit computations: an analytic calculation of the anyonic phases experienced by Abelian quasiholes; analytic relationships to the boundary Wess-Zumino-Witten model; and derivations of a wide class of QHE wavefunctions from a bulk field theory. We also further test the three-dimensional bosonization dualities in this new setting. Along the way, we accumulate new descriptions of the QHE. Finally, we turn away from flat space and investigate a problem in (3+1)-dimensional quantum gravity. We find that even as an effective theory, the theory has enough structure to suggest the inclusion of certain gravitational instantons in the path integral. An explicit computation in a minimally supersymmetric case illustrates the principles at work, and highlights the role of a hitherto unidentified scale in quantum gravity. It also is an interesting result in itself: a non-perturbative quantum instability of a flat supersymmetric Kaluza-Klein compactification.The author was supported by an STFC studentship and the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC grant agreement agreement STG 279943, “Strongly Coupled Systems”

Supersymmetry and String Theory

This text is an introduction to the fields of experimental and theoretical particle physics and cosmology. The book focuses on three principal areas: supersymmetry, string theory, and astrophysics and cosmology. The chapters on supersymmetry introduce the basics of supersymmetry and its phenomenology, and cover dynamics, dynamical supersymmetry breaking, and electric–magnetic duality. The book then introduces general relativity and the big bang theory, and the basic issues in inflationary cosmologies. The section on string theory discusses the spectra of known string theories, and the features of their interactions. Material added in the second edition includes the pivotal Higgs discovery and the results of the WMAP and Planck experiments. This book will be of great interest to graduates and researchers in the fields of particle theory, string theory, astrophysics, and cosmology. It has been reissued as an Open Access publication

Supersymmetry and String Theory

This text is an introduction to the fields of experimental and theoretical particle physics and cosmology. The book focuses on three principal areas: supersymmetry, string theory, and astrophysics and cosmology. The chapters on supersymmetry introduce the basics of supersymmetry and its phenomenology, and cover dynamics, dynamical supersymmetry breaking, and electric–magnetic duality. The book then introduces general relativity and the big bang theory, and the basic issues in inflationary cosmologies. The section on string theory discusses the spectra of known string theories, and the features of their interactions. Material added in the second edition includes the pivotal Higgs discovery and the results of the WMAP and Planck experiments. This book will be of great interest to graduates and researchers in the fields of particle theory, string theory, astrophysics, and cosmology. It has been reissued as an Open Access publication