arXiv subjects

Gabriele Travaglini

Publications and source records attributed to Gabriele Travaglini.

At least 73 records · Page 4Linked to original sources

arXiv2008

A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix

We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S-matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyse the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudo-conformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.

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arXiv2007

MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops

It is a remarkable fact that MHV amplitudes in maximally supersymmetric Yang-Mills theory at arbitrary loop order can be written as the product of the tree amplitude with the same helicity configuration and a universal, helicity-blind function of the kinematic invariants. In this note we show how for one-loop MHV amplitudes with an arbitrary number of external legs this universal function can be derived using Wilson loops. Our result is in precise agreement with the known expression for the infinite sequence of MHV amplitudes in N=4 super Yang-Mills. In the four-point case, we are able to reproduce the expression of the amplitude to all orders in the dimensional regularisation parameter epsilon. This prescription disentangles cleanly infrared divergences and finite terms, and leads to an intriguing one-to-one mapping between certain Wilson loop diagrams and (finite) two-mass easy box functions.

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arXiv2007

One-loop MHV Rules and Pure Yang-Mills

It has been known for some time that the standard MHV diagram formulation of perturbative Yang-Mills theory is incomplete, as it misses rational terms in one-loop scattering amplitudes of pure Yang-Mills. We propose that certain Lorentz violating counterterms, when expressed in the field variables which give rise to standard MHV vertices, produce precisely these missing terms. These counterterms appear when Yang-Mills is treated with a regulator, introduced by Thorn and collaborators, which arises in worldsheet formulations of Yang-Mills theory in the lightcone gauge. As an illustration of our proposal, we show that a simple one-loop, two-point counterterm is the generating function for the infinite sequence of one-loop, all-plus helicity amplitudes in pure Yang-Mills, in complete agreement with known expressions.

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arXiv2007

One-loop N=8 Supergravity Amplitudes from MHV Diagrams

We discuss the calculation of one-loop amplitudes in N=8 supergravity using MHV diagrams. In contrast to MHV amplitudes of gluons in Yang-Mills, tree-level MHV amplitudes of gravitons are not holomorphic in the spinor variables. In order to extend these amplitudes off shell, and use them as vertices to build loops, we introduce certain shifts for the spinor variables associated to the loop momenta. Using this off-shell prescription, we rederive the four-point MHV amplitude of gravitons at one loop, in complete agreement with known results. We also discuss the extension to the case of one-loop MHV amplitudes with an arbitrary number of gravitons.

hep-th↗

arXiv2007

Amplitudes in Pure Yang-Mills and MHV Diagrams

We show how to calculate the one-loop scattering amplitude with all gluons of negative helicity in non-supersymmetric Yang-Mills theory using MHV diagrams. We argue that the amplitude with all positive helicity gluons arises from a Jacobian which occurs when one performs a Backlund-type holomorphic change of variables in the lightcone Yang-Mills Lagrangian. This also results in contributions to scattering amplitudes from violations of the equivalence theorem. Furthermore, we discuss how the one-loop amplitudes with a single positive or negative helicity gluon arise in this formalism. Perturbation theory in the new variables leads to a hybrid of MHV diagrams and lightcone Yang-Mills theory.

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arXiv2007

Recursion Relations for One-Loop Gravity Amplitudes

We study the application of recursion relations to the calculation of finite one-loop gravity amplitudes. It is shown explicitly that the known four, five, and six graviton one-loop amplitudes for which the external legs have identical outgoing helicities, and the four graviton amplitude with helicities (-,+,+,+) can be derived from simple recursion relations. The latter amplitude is derived by introducing a one-loop three-point vertex of gravitons of positive helicity, which is the counterpart in gravity of the one-loop three-plus vertex in Yang-Mills. We show that new issues arise for the five point amplitude with helicities (-,+,+,+,+), where the application of known methods does not appear to work, and we discuss possible resolutions.

hep-th↗

arXiv2006

Quantum MHV Diagrams

Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method developed recently, the quantum MHV diagrams, and discuss applications to one-loop amplitudes. Furthermore, we briefly discuss the application of D-dimensional generalised unitarity to the calculation of scattering amplitudes in non-supersymmetric Yang-Mills.

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arXiv2005

Non-Supersymmetric Loop Amplitudes and MHV Vertices

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes - the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result.

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arXiv2005

A recursion relation for gravity amplitudes

Britto, Cachazo and Feng have recently derived a recursion relation for tree-level scattering amplitudes in Yang-Mills. This relation has a bilinear structure inherited from factorisation on multi-particle 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 tree-level scattering amplitude for n gravitons. Finally, we comment on the existence of recursion relations in general field theories.

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arXiv2005

Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity

We show how generalised unitarity cuts in D = 4 - 2 epsilon dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.

hep-th↗

arXiv2004

One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices

We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. This yields a new, simplified form for the MHV amplitudes, which is equivalent to the expressions obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.

hep-th↗

arXiv2004

A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory

We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.

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arXiv2004

Fermion BMN operators, the dilatation operator of N=4 SYM, and pp-wave string interactions

The goal of this paper is to study the BMN correspondence in the fermionic sector. On the field theory side, we compute matrix elements of the dilatation operator in N=4 Super Yang-Mills for BMN operators containing two fermion impurities. Our calculations are performed up to and including O(lambda') in the 't Hooft coupling and O(g_2) in the Yang-Mills genus counting parameter. On the string theory side, we compute the corresponding matrix elements of the interacting string Hamiltonian in string field theory, using the three-string interaction vertex constructed by Spradlin and Volovich (and subsequently elaborated by Pankiewicz and Stefanski). In string theory we use the natural string basis, and in field theory the basis which is isomorphic to it. We find that the matrix elements computed in field theory and the corresponding string amplitudes derived from the three-string vertex are, in all cases, in perfect agreement.

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arXiv2004

Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories

We study IR/UV mixing effects in noncommutative supersymmetric Yang-Mills theories with gauge group U(N) using background field perturbation theory. We compute three- and four-point functions of background fields, and show that the IR/UV mixed contributions to these correlators can be reproduced from an explicitly gauge-invariant effective action, which is expressed in terms of open Wilson lines.

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arXiv2003

New tests of the pp-wave correspondence

The pp-wave/SYM correspondence is an equivalence relation, H_{string}= Delta -J, between the Hamiltonian H_{string} of string field theory in the pp-wave background and the dilatation operator Delta in N=4 Super Yang-Mills in the double scaling limit. We calculate matrix elements of these operators in string field theory and in gauge theory.In the string theory Hilbert space we use the natural string basis,and in the gauge theory we use the basis which is isomorphic to it. States in this basis are specific linear combinations of the original BMN operators, and were constructed previously for the case of two scalar impurities. We extend this construction to incorporate BMN operators with vector and mixed impurities. This enables us to verify from the gauge theory perspective two key properties of the three-string interaction vertex of Spradlin and Volovich: (1) the vanishing of the three-string amplitude for string states with one vector and one scalar impurity; and (2) the relative minus sign in the string amplitude involving states with two vector impurities compared to that with two scalar impurities. This implies a spontaneous breaking of the Z_2 symmetry of the string field theory in the pp-wave background. Furthermore, we calculate the gauge theory matrix elements of Delta -J for states with an arbitrary number of scalar impurities. In all cases we find perfect agreement with the corresponding string amplitudes derived from the three-string vertex.

hep-th↗

arXiv2003

BMN operators with vector impurities, Z_2 symmetry and pp-waves

We calculate the coefficients of three-point functions of BMN operators with two vector impurities. We find that these coefficients can be obtained from those of the three-point functions of scalar BMN operators by interchanging the coefficient for the symmetric-traceless representation with the coefficient for the singlet. We conclude that the Z_2 symmetry of the pp-wave string theory is not manifest at the level of field theory three-point correlators.

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arXiv2002

PP-wave string interactions from n-point correlators of BMN operators

BMN operators are characterized by the fact that they have infinite R-charge and finite anomalous dimension in the BMN double scaling limit. Using this fact, we show that the BMN operators close under operator product expansion and form a sector in the N=4 supersymmetric Yang-Mills theory. We then identify short-distance limits of general BMN n-point correlators, and show how they correspond to the pp-wave string interactions. We also discuss instantons in the light of the pp-wave/SYM correspondence.

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arXiv2002

Three-point functions in N=4 Yang-Mills theory and pp-waves

Recently it has been proposed that the coefficient of the three-point function of the BMN operators in N=4 supersymmetric Yang-Mills theory is related to the three-string interactions in the pp-wave background. We calculate three-point functions of these operators to the first order in the effective Yang-Mills coupling lambda' = g_{YM}^2 N/J^2 in planar perturbation theory. On the string theory side, we derive the explicit expressions of the Neumann matrices to all orders in 1/(μp^+ α')^2. This allows us to compute the corresponding three-string scattering amplitudes. This provides an all orders prediction for the field theory three-point functions. We compare our field theory results with the string theory results to the subleading order in 1/(μp^+ α')^2 and find perfect agreement.

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