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Author: Francis Anthony Dolan
Publisher:
ISBN:
Category : Conformal invariants
Languages : en
Pages : 233
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Author: Francis Anthony Dolan
Publisher:
ISBN:
Category : Conformal invariants
Languages : en
Pages : 233
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Author: Muhammad Ali Shehper
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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We discuss four new problems in the subjects of superconformal field theories (SCFTs) and topological quantum field theories (TQFTs). In superconformal field theories, our focus is on N = 2 theories in four dimensions, where in the first two problems, we further narrow down to the case of “theories of class S”. First, we show that the previously known invariants used to classify theories of class S fail to distinguish many pairs of SCFTs in the ([doublestruck Z]2-twisted and untwisted) D-sector. We propose a new invariant, the global form of the flavor symmetry group, and show that it successfully distinguishes these pairs of theories. Next, we study the classification of SCFTs in the D4 sector of class S with nonabelian outer-automorphism twists around various cycles of the surface. We propose an extension of previous formulae for the superconformal index to cover this case and classify the SCFTs corresponding to fixtures (3-punctured spheres). We then go on to study families of SCFTs corresponding to once-punctured tori and 4-punctured spheres. We show that these families of SCFTs exhibit new behaviours, not seen in previous investigations. In particular, the generic theory with 4 punctures on the sphere from non-commuting [doublestruck Z]2 twisted sectors has six distinct weakly-coupled descriptions. In our third problem, we shift our focus to arbitrary N = 2 theories in 4d (i.e. not necessarily of class S). We show that if a 4d N = 2 is equipped with an N = (2, 2) supersymmetric surface defect, a marginal perturbation of the bulk theory induces a complex structure deformation of the defect moduli space. We describe a concrete way of computing this deformation using the bulk-defect OPE. For the fourth problem, we turn to the subject of topological quantum field theories. Here we study generalized discrete symmetries of two-dimensional semisimple TQFTs. We show that, in a special basis where the fusion rules of the TQFT are diagonalized, the 0-form symmetries act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. We use these results to study the equivariant Verlinde formula for general simple Lie groups. These formulae leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in special cases with low genus and SO(3) gauge group
Author: Kantaro Ohmori
Publisher: Springer
ISBN: 9811330921
Category : Science
Languages : en
Pages : 122
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This thesis describes the structures of six-dimensional (6d) superconformal field theories and its torus compactifications. The first half summarizes various aspects of 6d field theories, while the latter half investigates torus compactifications of these theories, and relates them to four-dimensional superconformal field theories in the class, called class S. It is known that compactifications of 6d conformal field theories with maximal supersymmetries provide numerous insights into four-dimensional superconformal field theories. This thesis generalizes the story to the theories with smaller supersymmetry, constructing those six-dimensional theories as brane configurations in the M-theory, and highlighting the importance of fractionalization of M5-branes. This result establishes new dualities between the theories with eight supercharges.
Author: Damien Calaque
Publisher: Springer
ISBN: 3319099493
Category : Science
Languages : en
Pages : 572
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Book Description
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Author: Akinori Tanaka
Publisher: Springer
ISBN: 9811013985
Category : Science
Languages : en
Pages : 91
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The author introduces the supersymmetric localization technique, a new approach for computing path integrals in quantum field theory on curved space (time) defined with interacting Lagrangian. The author focuses on a particular quantity called the superconformal index (SCI), which is defined by considering the theories on the product space of two spheres and circles, in order to clarify the validity of so-called three-dimensional mirror symmetry, one of the famous duality proposals. In addition to a review of known results, the author presents a new definition of SCI by considering theories on the product space of real-projective space and circles. In this book, he explains the concept of SCI from the point of view of quantum mechanics and gives localization computations by reducing field theoretical computations to many-body quantum mechanics. He applies his new results of SCI with real-projective space to test three-dimensional mirror symmetry, one of the dualities of quantum field theory. Real-projective space is known to be an unorientable surface like the Mobius strip, and there are many exotic effects resulting from Z2 holonomy of the surface. Thanks to these exotic structures, his results provide completely new evidence of three-dimensional mirror symmetry. The equivalence expected from three-dimensional mirror symmetry is transformed into a conjectural non-trivial mathematical identity through the new SCI, and he performs the proof of the identity using a q-binomial formula.
Author: Denis Bashkirov
Publisher:
ISBN:
Category : Quantum field theory
Languages : en
Pages : 0
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Author: H.C. Lee
Publisher: Springer Science & Business Media
ISBN: 1461309131
Category : Science
Languages : en
Pages : 594
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The Super Field Theory Workshop, held at Simon Fraser University, Vancouver, Canada July 25 - August 5, 1986 was originally intended to be a sequel to the 1983 Chalk River Workshop on Kaluza-Klein Theories and the 1985 Workshop on Quantum Field Theories held at the University of Western Ontario. The scope of the workshop was therefore not to be very big, with a program of about 20 papers, an anticipated 30 to 45 participants, and with much time scheduled for discussion and personal contact. These goals were soon changed in the face of wide interest in the workshop, both for participation and for giving talks, so that the workshop materialized with about 90 participants and 40 talks. This volume contains the texts, some considerably expanded from the oral version, of most of the talks pre sented at the workshop. Not included are a few talks whose manuscripts were not made available to the editors. In the last few years the subject of particle physics and unified field theory has developed in a way not witnessed in the last fifty years: a confluence with mathematics, especially in geometry, topology and algebra at an advanced level. This has vastly expanded the horizon of the disci pline and heightened the expectation that a true understanding of the fun damental laws of physics may soon be within reach. Most aspects of this new development are covered, many in pedagogical detail, by articles in this volume.
Author: Michio Kaku
Publisher: World Scientific
ISBN: 9814547298
Category :
Languages : en
Pages : 448
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Book Description
Frontiers in Quantum Field Theory is published in honor of Prof Keiji Kikkawa's 60th birthday. It deals with modern quantum field theory in the context of several exciting recent developments, many of them inspired or influenced by Prof Kikkawa's work, which include dualities in string theory and field theory, matrix models and noncritical strings, lower dimensional quantum gravity, topological and superconformal field theory.
Author: Emily Margaret Nardoni
Publisher:
ISBN:
Category :
Languages : en
Pages : 221
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In this dissertation we study properties of superconformal field theories (SCFTs) that arise from a variety of constructions. We begin with an extended review of various techniques in supersymmetry that are relevant throughout the work. In Chapter 3, we discuss aspects of theories with superpotentials given by Arnold's $A,D,E$ singularities, particularly the novelties that arise when the fields are matrices. We focus on four-dimensional $N=1$ variants of supersymmetric QCD, with $U(N_c)$ or $SU(N_c)$ gauge group, $N_f$ fundamental flavors, and adjoint matter fields $X$ and $Y$ appearing in $W_{A,D,E}(X,Y)$ superpotentials. We explore these issues by considering various deformations of the $W_{A,D,E}$ superpotentials, and the resulting RG flows and IR theories. In Chapter 4, we examine the infrared fixed points of four-dimensional $N=1$ supersymmetric $SU(2)$ gauge theory coupled to an adjoint and two fundamental chiral multiplets. We focus on a particular RG flow that leads to the $N=2$ Argyres-Douglas theory $H_0$, and a further deformation to an $N=1$ SCFT with low $a$ central charge. Then for the latter half of the dissertation we turn our attention to 4d SCFTs that arise from compactifications of M5-branes. In Chapter 6, we field-theoretically construct 4d $N=1$ quantum field theories by compactifying the 6d (2,0) theories on a Riemann surface with genus $g$ and $n$ punctures, where the normal bundle decomposes into a sum of two line bundles with possibly negative degrees $p$ and $q$. In Chapter 7, we study the 't Hooft anomalies of the SCFTs that arise from these compactifications. In general there are two independent contributions to the anomalies: there is a bulk term obtained by integrating the anomaly polynomial of the world-volume theory on the M5-branes over the Riemann surface, and there is a set of contributions due to local data at the punctures. Using anomaly inflow in M-theory, we describe how this general structure arises for cases when the four-dimensional theories preserve $N=2$ supersymmetry, and derive terms that account for the local data at the punctures.
Author: Konstantin Wiegandt
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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