arXiv subjects

Jan Plefka

Publications and source records attributed to Jan Plefka.

At least 73 records · Page 4Linked to original sources

arXiv2011

The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector

The dilatation operator of planar N=4 super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian acting on three adjacent scalar states. While four out of these follow from the known SU(2|3) sector two-loop dilatation operator, the remaining four coefficients are derived by diagrammatic techniques and a match to the known dimension of a length three primary operator. Finally, comments upon the use of this result for the evaluation of three-point structure functions of scalar operators at the one-loop order are given.

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arXiv2011

Coordinate representation of particle dynamics in AdS and in generic static spacetimes

We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature term. Our main emphasis is on AdS spaces, where this term is fixed by the isometry group. As a byproduct the isometry generators are constructed and the energy spectrum is reproduced. In the massless case the conformal symmetry is realized as well. We show the equivalence between this quantization and the covariant quantization, based on the Klein-Gordon type equation in AdS. We further demonstrate that the two quantization methods in an arbitrary (N+1)-dimensional static spacetime are equivalent to each other if the scalar curvature terms both in the operator E^2 and in the Klein-Gordon type equation have the same coefficient equal to (N-1)/(4N).

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arXiv2011

One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory

We report on a systematic study of scalar field three-point functions in planar SU(N) N=4 super Yang-Mills theory. The motivation for this work is to provide sufficient data for future conjectures on the higher-loop form of the structure constants possibly involving integrability. For this we have computed a sample of 70 structure constants at one-loop order involving primary operators of up to and including length five built entirely from scalar fields. We observe in all 17 cases occurring in our sample that the one-loop structure constant of two protected chiral primary operators and one unprotected operator is given by a simple linear function involving the anomalous scaling dimension of the latter. Moreover, a similar simple one-loop formula is proven for the three-point structure constants of the Konishi operator and two arbitrary protected or un-protected operators. It is again determined by the anomalous scaling dimensions of the operators involved.

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arXiv2011

All tree-level amplitudes in massless QCD

We derive compact analytical formulae for all tree-level color-ordered gauge theory amplitudes involving any number of external gluons and up to three massless quark-anti-quark pairs. A general formula is presented based on the combinatorics of paths along a rooted tree and associated determinants. Explicit expressions are displayed for the next-to-maximally helicity violating (NMHV) and next-to-next-to-maximally helicity violating (NNMHV) gauge theory amplitudes. Our results are obtained by projecting the previously-found expressions for the super-amplitudes of the maximally supersymmetric Yang-Mills theory (N=4 SYM) onto the relevant components yielding all gluon-gluino tree amplitudes in N=4 SYM. We show how these results carry over to the corresponding QCD amplitudes, including massless quarks of different flavors as well as a single electroweak vector boson. The public Mathematica package GGT is described, which encodes the results of this work and yields analytical formulae for all N=4 SYM gluon-gluino trees. These in turn yield all QCD trees with up to four external arbitrary-flavored massless quark-anti-quark-pairs.

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arXiv2011

On the Spectrum of the AdS_5xS^5 String at large lambda

We put forth a program for perturbatively quantizing the bosonic sector of the IIB superstring on AdS_5xS^5 in the large radius of curvature R (i.e. flat-space) limit, and in light-cone gauge. Using the quantization of the massive particle on AdS_5xS^5 as a guiding exercise, we read off the correct scaling of the particle coordinates in the large radius limit. In the corresponding large \sqrtλ=R^2/α' limit of the string the oscillator modes must be scaled differently from the zero modes. We compute the bosonic string Hamiltonian in this limit which gives the flat-space mass-squared operator at leading order, followed by a harmonic oscillator potential in the zero modes at subleading order. Using these ingredients we calculate the leading and sub-leading terms in the conformal dimension of the length-four Konishi state in the large-λlimit. Furthermore we work out the relevant terms of the energy expansion to next-to-next-to leading order, which are plagued by severe ordering ambiguities. This prevents us from determining the corrections to the spectrum at order λ^{-1/4}.

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arXiv2010

One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills

Recently it has been argued that tree-level scattering amplitudes in N=4 Yang-Mills theory are uniquely determined by a careful study of their superconformal and Yangian symmetries. However, at one-loop order these symmetries are known to become anomalous due to infrared divergences. We compute these one-loop anomalies for amplitudes defined through dimensional regularisation by studying the tree-level symmetry transformations of the unitarity branch cuts, keeping track of the crucial collinear terms arising from the holomorphic anomaly. We extract the superconformal anomalies and show that they may be cancelled through a universal one-loop deformation of the tree-level symmetry generators which involves only tree-level data. Specialising to the planar theory we also obtain the analogous deformation for the level-one Yangian generator of momentum. Explicit checks of our one-loop deformation are performed for MHV and the 6-point NMHV amplitudes.

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arXiv2010

Scattering into the fifth dimension of N=4 super Yang-Mills

We study an alternative to dimensional regularisation of planar scattering amplitudes in N=4 super Yang-Mills theory by going to the Coulomb phase of the theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism, allowing us to work in four dimensions. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. The latter acts on the kinematical variables of the amplitudes as well as on the Higgs masses in an effectively five dimensional space. We confirm this expectation by an explicit calculation in the gauge theory. A consequence of this exact dual conformal symmetry is a significantly reduced set of scalar basis integrals that are allowed to appear in an amplitude. For example, triangle sub-graphs are ruled out. We argue that the study of exponentiation of amplitudes is simpler in the Higgsed theory because evanescent terms in the mass regulator can be consistently dropped. We illustrate this by showing the exponentiation of a four-point amplitude to two loops. Finally, we also analytically compute the small mass expansion of a two-loop master integral with an internal mass.

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arXiv2009

Gravitational Contributions to the Running Yang-Mills Coupling in Large Extra-Dimensional Brane Worlds

We study the question of a modification of the running gauge coupling of Yang-Mills theories due to quantum gravitational effects in a compact large extra dimensional brane world scenario with a low energy quantum gravity scale. The ADD scenario is applied for a D=d+δdimensional space-time in which gravitons freely propagate, whereas the non-abelian gauge fields are confined to a d-dimensional brane. The extra dimensions are taken to be toroidal and the transverse fluctuation modes (branons) of the brane are taken into account. On this basis we have calculated the one-loop corrections due to virtual Kaluza-Klein graviton and branon modes for the gluon two- and three-point functions in an effective field theory treatment. Applying momentum cut-off regularization we find that for a d=4 brane the leading gravitational divergencies cancel irrespective of the number of extra dimensions δ, generalizing previous results in the absence of extra-dimensions. Hence, again the Yang-Mills β-function receives no gravitational corrections at one-loop. This is no longer true in a `universal' extra dimensional scenario with a d>4 dimensional brane. Moreover, the subleading power-law gravitational divergencies induce higher-dimensional counterterms, which we establish in our scheme. Interestingly, for d=4 these gravitationally induced counterterms are of the form recently considered in non-abelian Lee-Wick extensions of the standard model -- now with a possible mass scale in the TeV range due to the presence of large extra dimensions.

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arXiv2009

The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop

We develop a compact representation of the one-loop n-point functions of all chiral primary operators in planar SU(N), N=4 super Yang-Mills theory in terms of tree-level disk correlation functions and the scalar one-loop box integral. As a check, known results for all four-point functions and for n-point extremal and near-extremal correlators are rederived. The result is then used to evaluate explicitly a selection of five and six-point functions. Our findings suggest that a general one-loop five-point function may be represented through the minimal four-point and five-point functions of weight two operators.

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arXiv2009

Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills

In this paper we study the n-point correlation functions of two different families of local gauge invariant operators in N=4 supersymmetric Yang-Mills theory. The main idea is to consider the correlation functions of operators which all share a number of supersymmetries irrespective of their relative locations. We achieve this by equipping the operators with explicit space-time dependence. We provide evidence by different methods that these n-point correlators do not receive quantum corrections in perturbation theory and are hence given exactly by their tree-level result. The arguments rely on explicit checks for general four-point correlators, some five-point and six-point correlators and a more abstract calculation based on a novel topological twisting of N=4 supersymmetric Yang-Mills theory.

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arXiv2008

Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.

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arXiv2008

M-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions

We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D=11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant gauge flux, which are described in terms of an arbitrary holomorphic function of the complexified 6 dimensional space. The supermembrane and matrix theory descriptions are also provided and we identify the relevant supersymmetry transformation rules. The action also arises through a dimensional reduction of N=1, D=4 supersymmetric Yang-Mills theory coupled to 3 gauge adjoint and chiral multiplets, whose interactions are determined by the holomorphic function of the supergravity solution now constituting the superpotential.

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arXiv2007

Absence of gravitational contributions to the running Yang-Mills coupling

The question of a modification of the running gauge coupling of (non-) abelian gauge theories by an incorporation of the quantum gravity contribution has recently attracted considerable interest. In this letter we perform an involved diagrammatical calculation in the full Einstein-Yang-Mills system both in cut-off and dimensional regularization at one loop order. It is found that all gravitational quadratic divergencies cancel in cut-off regularization and are trivially absent in dimensional regularization so that there is no alteration to asymptotic freedom at high energies. The logarithmic divergencies give rise to an extended effective Einstein-Yang-Mills Lagrangian with a counterterm of dimension six. In the pure Yang-Mills sector this counterterm can be removed by a nonlinear field redefinition of the gauge potential, reproducing a classical result of Deser, Tsao and van Nieuwenhuizen obtained in the background field method with dimensional regularization.

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arXiv2007

Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring

We perform a detailed test of the quantum integrability of the AdS_5 x S^5 superstring in uniform light-cone gauge in its near plane-wave limit. For this we establish the form of the general nested light-cone Bethe equations for the quantum string from the long range psu(2,2|4) Bethe equations of Beisert and Staudacher. Moreover the scheme for translating excited string states into Bethe root excitations is given. We then confront the direct perturbative diagonalization of the light-cone string Hamiltonian in the near plane-wave limit with the energy spectrum obtained from the general nested light-cone Bethe equations in various higher rank sectors. The analysis is performed both analytically and numerically up to the level of six impurity states and subsectors of maximal rank four. We find perfect agreement in all cases lending strong support to the quantum integrability of the AdS_5 x S^5 superstring.

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arXiv2006

The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N=4 gauge theory.

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arXiv2006

On the Hopf algebra structure of the AdS/CFT S-matrix

We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1|2) subsector due to Janik to the full algebra by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by length-changing effects and results in an unusual central braiding. As an application we explicitly determine the antiparticle representation by means of the established antipode.

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arXiv2006

The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We then quantize the theory perturbatively in the near plane-wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all loop) dilatation operators in the dual N=4 gauge theory.

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arXiv2005

Spinning strings and integrable spin chains in the AdS/CFT correspondence

In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display its reformulation in terms of a Heisenberg s=1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way we comment on further developments and generalizations of the subject and point to the relevant literature.

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