Physical Mathematics and the Future
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Gravitational Anomaly and Hawking Radiation of Apparent Horizon in FRW Universe
Eur. Phys. J. C (2009) 62: 455–458 DOI 10.1140/epjc/s10052-009-1081-4 Letter Gravitational anomaly and Hawking radiation of apparent horizon in FRW universe Ran Lia, Ji-Rong Renb, Shao-Wen Wei Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, Gansu, China Received: 27 February 2009 / Published online: 26 June 2009 © Springer-Verlag / Società Italiana di Fisica 2009 Abstract Motivated by the successful applications of the have been carried out [8–28]. In fact, the anomaly analy- anomaly cancellation method to derive Hawking radiation sis can be traced back to Christensen and Fulling’s early from various types of black hole spacetimes, we further work [29], in which they suggested that there exists a rela- extend the gravitational anomaly method to investigate the tion between the Hawking radiation and the anomalous trace Hawking radiation from the apparent horizon of a FRW uni- of the field under the condition that the covariant conser- verse by assuming that the gravitational anomaly also exists vation law is valid. Imposing boundary condition near the near the apparent horizon of the FRW universe. The result horizon, Wilczek et al. showed that Hawking radiation is shows that the radiation flux from the apparent horizon of just the cancel term of the gravitational anomaly of the co- the FRW universe measured by a Kodama observer is just variant conservation law and gauge invariance. Their basic the pure thermal flux. The result presented here will further idea is that, near the horizon, a quantum field in a black hole confirm the thermal properties of the apparent horizon in a background can be effectively described by an infinite col- FRW universe. -
JHEP05(2015)095 ) Gauge Springer N May 4, 2015 May 19, 2015 : : February 11, 2015
Published for SISSA by Springer Received: February 11, 2015 Accepted: May 4, 2015 Published: May 19, 2015 Defects and quantum Seiberg-Witten geometry JHEP05(2015)095 Mathew Bullimore,a Hee-Cheol Kimb and Peter Koroteevb aInstitute for Advanced Study, Einstein Dr., Princeton, NJ 08540, U.S.A. bPerimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L2Y5, Canada E-mail: [email protected], [email protected], [email protected] Abstract: We study the Nekrasov partition function of the five dimensional U(N) gauge theory with maximal supersymmetry on R4 S1 in the presence of codimension two defects. × The codimension two defects can be described either as monodromy defects, or by coupling to a certain class of three dimensional quiver gauge theories on R2 S1. We explain how × these computations are connected with both classical and quantum integrable systems. We check, as an expansion in the instanton number, that the aforementioned partition functions are eigenfunctions of an elliptic integrable many-body system, which quantizes the Seiberg-Witten geometry of the five-dimensional gauge theory. Keywords: Supersymmetric gauge theory, Duality in Gauge Field Theories, Integrable Equations in Physics, Differential and Algebraic Geometry ArXiv ePrint: 1412.6081 Open Access, c The Authors. ⃝ doi:10.1007/JHEP05(2015)095 Article funded by SCOAP3. Contents 1 Introduction 1 2 Twisted chiral rings 3 2.1 The Nekrasov-Shatashvili correspondence 4 2.2 Quantum/classical duality 6 2.2.1 Electric frame -
Chiral Currents from Anomalies
ω2 α 2 ω1 α1 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 1 Chiral currents from Anomalies Michael Stone Institute for Condensed Matter Theory University of Illinois Santa-Fe July 18 2018 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 2 Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 3 Experiment aims to verify: k ρσαβ r T µν = F µνJ − p r [F Rνµ ]; µ µ 384π2 −g µ ρσ αβ k µνρσ k µνρσ r J µ = − p F F − p Rα Rβ ; µ 32π2 −g µν ρσ 768π2 −g βµν αρσ Here k is number of Weyl fermions, or the Berry flux for a single Weyl node. Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 4 What the experiment measures Contribution to energy current for 3d Weyl fermion with H^ = σ · k µ2 1 J = B + T 2 8π2 24 Simple explanation: The B field makes B=2π one-dimensional chiral fermions per unit area. These have = +k Energy current/density from each one-dimensional chiral fermion: Z 1 d 1 µ2 1 J = − θ(−) = 2π + T 2 β(−µ) 2 −∞ 2π 1 + e 8π 24 Could even have been worked out by Sommerfeld in 1928! Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 5 Are we really exploring anomaly physics? Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 6 Yes! Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 7 Energy-Momentum Anomaly k ρσαβ r T µν = F µνJ − p r [F Rνµ ]; µ µ 384π2 −g µ ρσ αβ Michael Stone (ICMT ) Chiral Currents Santa-Fe July 18 2018 8 Origin of Gravitational Anomaly in 2 dimensions Set z = x + iy and use conformal coordinates ds2 = expfφ(z; z¯)gdz¯ ⊗ dz Example: non-chiral scalar field '^ has central charge c = 1 and energy-momentum operator is T^(z) =:@z'@^ z'^: Actual energy-momentum tensor is c T = T^(z) + @2 φ − 1 (@ φ)2 zz 24π zz 2 z c T = T^(¯z) + @2 φ − 1 (@ φ)2 z¯z¯ 24π z¯z¯ 2 z¯ c T = − @2 φ zz¯ 24π zz¯ z z¯ Now Γzz = @zφ, Γz¯z¯ = @z¯φ, all others zero. -
Social Choice Theory Christian List
1 Social Choice Theory Christian List Social choice theory is the study of collective decision procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members’ individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems. Pioneered in the 18th century by Nicolas de Condorcet and Jean-Charles de Borda and in the 19th century by Charles Dodgson (also known as Lewis Carroll), social choice theory took off in the 20th century with the works of Kenneth Arrow, Amartya Sen, and Duncan Black. Its influence extends across economics, political science, philosophy, mathematics, and recently computer science and biology. Apart from contributing to our understanding of collective decision procedures, social choice theory has applications in the areas of institutional design, welfare economics, and social epistemology. 1. History of social choice theory 1.1 Condorcet The two scholars most often associated with the development of social choice theory are the Frenchman Nicolas de Condorcet (1743-1794) and the American Kenneth Arrow (born 1921). -
TASI Lectures on String Compactification, Model Building
CERN-PH-TH/2005-205 IFT-UAM/CSIC-05-044 TASI lectures on String Compactification, Model Building, and Fluxes Angel M. Uranga TH Unit, CERN, CH-1211 Geneve 23, Switzerland Instituto de F´ısica Te´orica, C-XVI Universidad Aut´onoma de Madrid Cantoblanco, 28049 Madrid, Spain angel.uranga@cern,ch We review the construction of chiral four-dimensional compactifications of string the- ory with different systems of D-branes, including type IIA intersecting D6-branes and type IIB magnetised D-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Stan- dard Model, and review their main phenomenological properties. We finally describe how to implement the tecniques to construct these models in flux compactifications, leading to models with realistic gauge sectors, moduli stabilization and supersymmetry breaking soft terms. Lecture 1. Model building in IIA: Intersecting brane worlds 1 Introduction String theory has the remarkable property that it provides a description of gauge and gravitational interactions in a unified framework consistently at the quantum level. It is this general feature (beyond other beautiful properties of particular string models) that makes this theory interesting as a possible candidate to unify our description of the different particles and interactions in Nature. Now if string theory is indeed realized in Nature, it should be able to lead not just to `gauge interactions' in general, but rather to gauge sectors as rich and intricate as the gauge theory we know as the Standard Model of Particle Physics. -
Christopher Elliott
Christopher Elliott Contact Details Full Name Christopher James Elliott Date of Birth 20th Sep, 1987 Nationality British Contact Address University of Massachusetts Department of Mathematics and Statistics 710 N Pleasant St Amherst, MA 01003 USA E-mail Address [email protected] Work Experience 2019– Visiting Assistant Professor, University of Massachusetts, Amherst 2016–2019 Postdoctoral Fellow, Institut des Hautes Etudes´ Scientifiques Education 2010–2016 PhD, Northwestern University Advisors: Kevin Costello and David Nadler Thesis Title: Gauge Theoretic Aspects of the Geometric Langlands Correspondence. 2009–2010 MMath (Mathematics Tripos: Part III), University of Cambridge, With Distinction. Part III Essay: D-Modules and Hodge Theory 2006–2009 BA (hons) (Mathematics), University of Cambridge, 1st Class. Research Visits 2014–2018 Perimeter Institute (7 visits, each 1-3 weeks) Oct–Nov 2017 MPIM, Bonn Oct 2017 Hausdorff Institute, Bonn Nov 2016 MPIM, Bonn Research Interests I’m interested in mathematical aspects and applications of quantum field theory. In particular • The construction and classification of (not necessarily topological) twists of classical and quantum field theories, especially using techniques of derived algebraic geometry and homotopical algebra. • The connection between structures appearing in various versions of the geometric Langlands correspon- dence and twists of four-, five- and six-dimensional supersymmetric gauge theories. • The theory of factorization algebras as a model for perturbative quantum field theory, possibly with bound- ary conditions and defects. Publications and Preprints 1. Quantum Geometric Langlands Categories from N = 4 Super Yang–Mills Theory (joint with Philsang Yoo), arXiv:2008.10988 2. Spontaneous Symmetry Breaking: a View from Derived Geometry (joint with Owen Gwilliam), Journal of Geometry and Physics, Vol 162, 2021, arXiv:2008.02302 1 3. -
Scientists Observe Gravitational Anomaly on Earth 21 July 2017
Scientists observe gravitational anomaly on Earth 21 July 2017 strange that they named this phenomenon an "anomaly." For most of their history, these quantum anomalies were confined to the world of elementary particle physics explored in huge accelerator laboratories such as Large Hadron Collider at CERN in Switzerland. Now however, a new type of materials, the so-called Weyl semimetals, similar to 3-D graphene, allow us to put the symmetry destructing quantum anomaly to work in everyday phenomena, such as the creation of electric current. In these exotic materials electrons effectively behave in the very same way as the elementary Prof. Dr. Karl Landsteiner, a string theorist at the particles studied in high energy accelerators. These Instituto de Fisica Teorica UAM/CSIC and co-author of particles have the strange property that they cannot the paper made this graphic to explain the gravitational be at rest—they have to move with a constant speed anomaly. Credit: IBM Research at all times. They also have another property called spin. It is like a tiny magnet attached to the particles and they come in two species. The spin can either point in the direction of motion or in the opposite Modern physics has accustomed us to strange and direction. counterintuitive notions of reality—especially quantum physics which is famous for leaving physical objects in strange states of superposition. For example, Schrödinger's cat, who finds itself unable to decide if it is dead or alive. Sometimes however quantum mechanics is more decisive and even destructive. Symmetries are the holy grail for physicists. -
S-Duality in N=1 Orientifold Scfts
S-duality in = 1 orientifold SCFTs N Iñaki García Etxebarria 1210.7799, 1307.1701 with B. Heidenreich and T. Wrase and 1506.03090, 1612.00853, 18xx.xxxxx with B. Heidenreich 3 Intro C =Z3 C(dP 1) General Conclusions Montonen-Olive = 4 (S-)duality N Given a 4d = 4 field theory with gauge group G and gauge N coupling τ = θ + i=g2 (*), there is a completely equivalent description with gauge group G and coupling 1/τ (for θ = 0 this _ − is g 1=g). Examples: $ G G_ U(1) U(1) U(N) U(N) SU(N) SU(N)=ZN SO(2N) SO(2N) SO(2N + 1) Sp(2N) Very non-perturbative duality, exchanges electrically charged operators with magnetically charged ones. (*) I will not describe global structure or line operators here. 3 Intro C =Z3 C(dP 1) General Conclusions S-duality u = 1+iτ j(τ) i+τ j j In this representation τ 1/τ is u u. ! − ! − 3 Intro C =Z3 C(dP 1) General Conclusions S-duality in < 4 N Three main ways of generalizing = 4 S-duality: N Trace what relevant susy-breaking deformations do in different duality frames. [Argyres, Intriligator, Leigh, Strassler ’99]... Make a guess [Seiberg ’94]. Identify some higher principle behind = 4 S-duality, and find backgrounds with less susy that followN the same principle. (2; 0) 6d theory on T 2 Riemann surfaces. [Gaiotto ’09], ..., [Gaiotto, Razamat! ’15], [Hanany, Maruyoshi ’15],... Field theory S-duality from IIB S-duality. 3 Intro C =Z3 C(dP 1) General Conclusions Field theories from solitons One way to construct four dimensional field theories from string theory is to build solitons with a four dimensional core. -
Jhep05(2019)105
Published for SISSA by Springer Received: March 21, 2019 Accepted: May 7, 2019 Published: May 20, 2019 Modular symmetries and the swampland conjectures JHEP05(2019)105 E. Gonzalo,a;b L.E. Ib´a~neza;b and A.M. Urangaa aInstituto de F´ısica Te´orica IFT-UAM/CSIC, C/ Nicol´as Cabrera 13-15, Campus de Cantoblanco, 28049 Madrid, Spain bDepartamento de F´ısica Te´orica, Facultad de Ciencias, Universidad Aut´onomade Madrid, 28049 Madrid, Spain E-mail: [email protected], [email protected], [email protected] Abstract: Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular symmetries of the moduli effective action to check swampland constraints beyond perturbation theory. As an example we study the case of heterotic 4d N = 1 compactifications, whose non-perturbative effective action is known to be invariant under modular symmetries acting on the K¨ahler and complex structure moduli, in particular SL(2; Z) T-dualities (or subgroups thereof) for 4d heterotic or orbifold compactifications. Remarkably, in models with non-perturbative superpotentials, the corresponding duality invariant potentials diverge at points at infinite distance in moduli space. The divergence relates to towers of states becoming light, in agreement with the distance conjecture. We discuss specific examples of this behavior based on gaugino condensation in heterotic orbifolds. We show that these examples are dual to compactifications of type I' or Horava-Witten theory, in which the SL(2; Z) acts on the complex structure of an underlying 2-torus, and the tower of light states correspond to D0-branes or M-theory KK modes. -
String Creation and Heterotic–Type I' Duality
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server hep-th/9711098 HUTP-97/A048 DAMTP-97-119 PUPT-1730 String Creation and Heterotic–Type I’ Duality Oren Bergman a∗, Matthias R. Gaberdiel b† and Gilad Lifschytz c‡ a Lyman Laboratory of Physics Harvard University Cambridge, MA 02138 b Department of Applied Mathematics and Theoretical Physics Cambridge University Silver Street Cambridge, CB3 9EW U. K. c Joseph Henry Laboratories Princeton University Princeton, NJ 08544 November 1997 Abstract The BPS spectrum of type I’ string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I’, and it is demonstrated that the relevant states in type I’ preserve supersym- metry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the D0-D8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I’, and on the predictions for the quantum mechanics of type I’ D0-branes. ∗E-mail address: [email protected] †E-mail address: [email protected] ‡E-mail address: [email protected] 1 Introduction An interesting phenomenon involving crossing D-branes has recently been discovered [1, 2, 3]. When a Dp-brane and a D(8 − p)-brane that are mutually transverse cross, a fundamental string is created between them. This effect is related by U-duality to the creation of a D3- brane when appropriately oriented Neveu-Schwarz and Dirichlet 5-branes cross [4]. -
Mathematics and Materials
IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics 10.1090/pcms/023 Mathematics and Materials IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics Rafe Mazzeo, Series Editor Mark J. Bowick, David Kinderlehrer, Govind Menon, and Charles Radin, Volume Editors. IAS/Park City Mathematics Institute runs mathematics education programs that bring together high school mathematics teachers, researchers in mathematics and mathematics education, undergraduate mathematics faculty, graduate students, and undergraduates to participate in distinct but overlapping programs of research and education. This volume contains the lecture notes from the Graduate Summer School program 2010 Mathematics Subject Classification. Primary 82B05, 35Q70, 82B26, 74N05, 51P05, 52C17, 52C23. Library of Congress Cataloging-in-Publication Data Names: Bowick, Mark J., editor. | Kinderlehrer, David, editor. | Menon, Govind, 1973– editor. | Radin, Charles, 1945– editor. | Institute for Advanced Study (Princeton, N.J.) | Society for Industrial and Applied Mathematics. Title: Mathematics and materials / Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin, editors. Description: [Providence] : American Mathematical Society, [2017] | Series: IAS/Park City math- ematics series ; volume 23 | “Institute for Advanced Study.” | “Society for Industrial and Applied Mathematics.” | “This volume contains lectures presented at the Park City summer school on Mathematics and Materials in July 2014.” – Introduction. | Includes bibliographical references. Identifiers: LCCN 2016030010 | ISBN 9781470429195 (alk. paper) Subjects: LCSH: Statistical mechanics–Congresses. -
Msc in Applied Mathematics
MSc in Applied Mathematics Title: Past, Present and Challenges in Yang-Mills Theory Author: José Luis Tejedor Advisor: Sebastià Xambó Descamps Department: Departament de Matemàtica Aplicada II Academic year: 2011-2012 PAST, PRESENT AND CHALLENGES IN YANG-MILLS THEORY Jos´eLuis Tejedor June 11, 2012 Abstract In electrodynamics the potentials are not uniquely defined. The electromagnetic field is un- changed by gauge transformations of the potential. The electromagnestism is a gauge theory with U(1) as gauge group. C. N. Yang and R. Mills extended in 1954 the concept of gauge theory for abelian groups to non-abelian groups to provide an explanation for strong interactions. The idea of Yang-Mills was criticized by Pauli, as the quanta of the Yang-Mills field must be massless in order to maintain gauge invariance. The idea was set aside until 1960, when the concept of particles acquiring mass through symmetry breaking in massless theories was put forward. This prompted a significant restart of Yang-Mills theory studies that proved succesful in the formula- tion of both electroweak unification and quantum electrodynamics (QCD). The Standard Model combines the strong interaction with the unified electroweak interaction through the symmetry group SU(3) ⊗ SU(2) ⊗ U(1). Modern gauge theory includes lattice gauge theory, supersymme- try, magnetic monopoles, supergravity, instantons, etc. Concerning the mathematics, the field of Yang-Mills theories was included in the Clay Mathematics Institute's list of \Millenium Prize Problems". This prize-problem focuses, especially, on a proof of the conjecture that the lowest excitations of a pure four-dimensional Yang-Mills theory (i.e.