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365
Large N field theories, string theory and gravity
, 2001
"... We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evide ..."
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Cited by 1474 (45 self)
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We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Antide Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and nonconformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 397 (26 self)
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A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 299 (25 self)
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We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior antide Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N = 4 gauged supergravity theory holographically dual to a sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a cfunction that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the cfunction coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.
Noncommutative Renormalization
 SÉMINAIRE POINCARÉ X (2007) 1 – 81
, 2007
"... A new version of scale analysis and renormalization theory has been found on the noncommutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on noncommutative tha ..."
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Cited by 169 (28 self)
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A new version of scale analysis and renormalization theory has been found on the noncommutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on noncommutative than on ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore be an alternative to supersymmetry. We review this rapidly growing subject.
Dbranes, tachyons, and string field theory
, 2003
"... In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten’s cubic bosonic open string field theory. We use both the lowenergy YangMills description and the language of string field theory to explain the problem of tachyon condensation on unstable Dbra ..."
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Cited by 76 (4 self)
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In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten’s cubic bosonic open string field theory. We use both the lowenergy YangMills description and the language of string field theory to explain the problem of tachyon condensation on unstable Dbranes. We give a selfcontained introduction to open string field theory using both conformal field theory and overlap integrals. Our main subjects are the Sen conjectures on tachyon condensation in open string field theory and the evidence that supports these conjectures. We conclude with a discussion of vacuum string field theory and projectors of the staralgebra of open string fields. We comment on the possible role of string field theory in the construction of a nonperturbative formulation of string theory that captures all possible string backgrounds.
The standard model on noncommutative spacetime
 PHYS. J. C23
"... We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard ..."
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Cited by 62 (5 self)
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We consider the Standard Model on a noncommutative space and expand the action in the noncommutativity parameter θ µν. No new particles are introduced, the structure group is SU(3) × SU(2) × U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary Standard Model. At leading order in θ µν we find new vertices which are absent in the Standard Model on commutative spacetime. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in noncommutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the
Exact solution of quantum field theory on noncommutative phase spaces
 017, 2004, hepth/0308043. – 43
"... We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s fun ..."
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Cited by 59 (6 self)
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We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the GroenewoldMoyal starproduct. Explicit results are presented for all Green’s functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed nonperturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinitedimensional noncommutative algebra.
The spectral action for Moyal planes
 J. Math. Phys
"... Extending a result of D. V. Vassilevich [50], we obtain the asymptotic expansion for the trace of a spatially regularized heat operator LΘ (f)e−t△Θ, where △Θ is a generalized Laplacian defined with Moyal products and LΘ (f) is Moyal left multiplication. The Moyal planes corresponding to any skewsymm ..."
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Cited by 44 (10 self)
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Extending a result of D. V. Vassilevich [50], we obtain the asymptotic expansion for the trace of a spatially regularized heat operator LΘ (f)e−t△Θ, where △Θ is a generalized Laplacian defined with Moyal products and LΘ (f) is Moyal left multiplication. The Moyal planes corresponding to any skewsymmetric matrix Θ being spectral triples [24], the spectral action introduced in noncommutative geometry by A. Chamseddine and A. Connes [6] is computed. This result generalizes the ConnesLott action [15] previously computed by Gayral [23] for symplectic Θ.
Topological strings in generalized complex space
"... A twodimensional topological sigmamodel on a generalized CalabiYau target space X is defined. The model is constructed in BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction the algebra of Qtransformations automatically ..."
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Cited by 40 (1 self)
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A twodimensional topological sigmamodel on a generalized CalabiYau target space X is defined. The model is constructed in BatalinVilkovisky formalism using only a generalized complex structure J and a pure spinor ρ on X. In the present construction the algebra of Qtransformations automatically closes offshell, the model transparently depends only on J, the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted N = 2 CFT can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector β and recover holomorphic noncommutative Kontsevich ∗product. 1
Noncommutative Induced Gauge Theory
, 2007
"... We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4dimensional Moyal space and compute in position space the oneloop YangMillstype effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action ..."
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Cited by 38 (10 self)
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We consider an external gauge potential minimally coupled to a renormalisable scalar theory on 4dimensional Moyal space and compute in position space the oneloop YangMillstype effective theory generated from the integration over the scalar field. We find that the gauge invariant effective action involves, beyond the expected noncommutative version of the pure YangMills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic oscillator term, which for the noncommutative ϕ 4theory on Moyal space ensures renormalisability. The expression of a possible candidate for a renormalisable action for a gauge theory defined on Moyal space is conjectured and discussed.