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1,012
ElectricMagnetic duality and the geometric Langlands program
, 2006
"... The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t H ..."
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Cited by 300 (26 self)
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The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super YangMills theory in four dimensions. The key ingredients are electricmagnetic duality of gauge theory, mirror symmetry of sigmamodels, branes, Wilson and ’t Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke
A Supersymmetry Primer
, 2011
"... I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction ..."
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Cited by 232 (2 self)
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I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetrybreaking interactions, the Minimal Supersymmetric Standard Model (MSSM), Rparity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.
Spin Foam Models for Quantum Gravity
, 2008
"... In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. R ..."
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Cited by 126 (8 self)
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In this article we review the present status of the spin foam formulation of nonperturbative (background independent) quantum gravity. The article is divided in two parts. In the first part we present a general introduction to the main ideas emphasizing their motivations from various perspectives. Riemannian 3dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for 4dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc.). In the second part we concentrate on the definition of the BarrettCrane model. We present the main results obtained in this framework from a critical perspective. Finally we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the BarrettCrane model in this framework and review the finiteness results obtained for both its Riemannian as well
Symmetry breaking and axionic strings in the warped deformed conifold
 JHEP 0409
"... We interpret Dstrings at the bottom of the warped deformed conifold as axionic strings in the dual cascading SU(N + M) × SU(N) gauge theory. The axion is a massless pseudoscalar glueball which we find in the supergravity fluctuation spectrum and interpret as the Goldstone boson of spontaneously b ..."
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Cited by 74 (10 self)
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We interpret Dstrings at the bottom of the warped deformed conifold as axionic strings in the dual cascading SU(N + M) × SU(N) gauge theory. The axion is a massless pseudoscalar glueball which we find in the supergravity fluctuation spectrum and interpret as the Goldstone boson of spontaneously broken U(1) baryon number symmetry. The existence of this massless glueball, anticipated in hepth/0101013, supports the idea that the cascading gauge theory is on the baryonic branch, i.e. the U(1)B global symmetry is broken by expectation values of baryonic operators. We also find a massless scalar glueball, which is a superpartner of the pseudoscalar. This scalar mode is a mixture of an NSNS 2form and a metric perturbation of the warped deformed conifold of a type first considered in hepth/0012034.
Weak Hamiltonian, CP violation and rare decays
, 1998
"... These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dim ..."
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Cited by 67 (8 self)
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These lectures describe in detail the effective Hamiltonians for weak decays of mesons constructed by means of the operator product expansion and the renormalization group method. We calculate Wilson coeffcients of local operators, discuss mixing of operators under renormalization, the anomalous dimensions of operators and anomalous dimension matrices. We elaborate on the renormalzation scheme and renormalization scale dependences and their cancellations in physical amplitudes. In particular we discuss the issue of γ5 in Ddimensions and the role of evanescent operators in the calculation of twoloop anomalous dimensions. We present an explicit calculation of the 6 × 6 oneloop anomalous dimension matrix involving currentcurrent and QCDpenguin operators and we give some hints how to properly calculate twoloop anomalous dimensions of these operators. In the phenonomenological part of these lectures we discuss in detail: CKM matrix, the unitarity triangle and its determination, twobody nonleptonic Bdecays and the generalized factorization, the ratio ε ′/ε, B → Xsγ, K + → π + ν¯ν, KL → π 0 ν¯ν, B → Xsν¯ν, Bs → µ¯µ and some aspects of CP violation in
Consistent interactions between gauge fields: the cohomological approach
 In Henneaux et al. [54
"... Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré i ..."
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Cited by 63 (2 self)
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Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the YangMills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the YangMills coupling is therefore rederived through cohomological arguments. 1.
Twocomponent spinor techniques and Feynman rules for quantum field theory and supersymmetry
, 2008
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What do CFTs tell us about antide Sitter spacetimes
 hepth/9902052, JHEP 9903:001
, 1999
"... The AdS/CFT conjecture relates quantum gravity on Antide Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk Smatrix. Our first approach finds the bulk Smatrix as a limit of scattering from an AdS b ..."
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Cited by 53 (10 self)
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The AdS/CFT conjecture relates quantum gravity on Antide Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk Smatrix. Our first approach finds the bulk Smatrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.
A recursion relation for gravity amplitudes
 NUCL. PHYS. B
, 2005
"... Britto, Cachazo and Feng have recently derived a recursion relation for treelevel scattering amplitudes in YangMills. This relation has a bilinear structure inherited from factorisation on multiparticle poles of the scattering amplitudes – a rather generic feature of field theory. Motivated by th ..."
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Cited by 43 (8 self)
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Britto, Cachazo and Feng have recently derived a recursion relation for treelevel scattering amplitudes in YangMills. This relation has a bilinear structure inherited from factorisation on multiparticle poles of the scattering amplitudes – a rather generic feature of field theory. Motivated by this, we propose a new recursion relation for scattering amplitudes of gravitons at tree level. Using this recursion relation, we derive a new general formula for the MHV treelevel scattering amplitude for n gravitons. Finally, we comment on the existence of recursion relations in general field theories.