arXiv subjects

Andreas Brandhuber

Publications and source records attributed to Andreas Brandhuber.

70 records · Page 4Linked to original sources

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗

arXiv2004

Chiral Rings, Superpotentials and the Vacuum Structure of N=1 Supersymmetric Gauge Theories

We use the Konishi anomaly equations to construct the exact effective superpotential of the glueball superfields in various N=1 supersymmetric gauge theories. We use the superpotentials to study in detail the structure of the spaces of vacua of these theories. We consider chiral and non-chiral SU(N) models, the exceptional gauge group G(2) and models that break supersymmetry dynamically.

hep-th↗

arXiv2002

Matter From G(2) Manifolds

We describe how chiral matter charged under SU(N) and SO(2N) gauge groups arises from codimension seven singularities in compactifications of M-theory on manifolds with G(2) holonomy. The geometry of these spaces is that of a cone over a six-dimensional Einstein space which can be constructed by (multiple) unfolding of hyper-Kahler quotient spaces. In type IIA the corresponding picture is given by stacks of intersecting D6-branes and chiral matter arises from open strings stretching between them. Usually one obtains (bi)fundamental representations but by including orientifold six-planes in the type IIA picture we find more exotic representations like the anti-symmetric, which is important for the study of SU(5) grand unification, and trifundamental representations. We also exhibit many cases where the G(2) metrics can be described explicitly, although in general the metrics on the spaces constructed via unfolding are not known.

hep-th↗

arXiv2002

G(2) Holonomy Spaces from Invariant Three-Forms

We construct several new G(2) holonomy metrics that play an important role in recent studies of geometrical transitions in compactifications of M-theory to four dimensions. In type IIA string theory these metrics correspond to D6 branes wrapped on the three-cycle of the deformed conifold and the resolved conifold with two-form RR flux on the blown-up two-sphere, which are related by a conifold transition. We also study a G(2) metric that is related in type IIA to the line bundle over S^2 x S^2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G(2) structures in terms of three-forms which are closed and co-closed. Besides being an elegant formalism this turns out to be a practical tool to construct G(2) holonomy metrics.

hep-th↗

arXiv2001

Current correlators in the Coulomb branch of N=4 SYM

We study correlators of R-symmetry currents in the Coulomb branch of N = 4 supersymmetric gauge theory in the large-N limit, using the AdS/CFT correspondence. In particular, we consider gauge fields in the presence of gravity and scalar fields parameterizing the coset SL(6,R)/SO(6) in the context of five-dimensional gauged supergravity. From a ten-dimensional point of view these backgrounds correspond to continuous D3-brane distributions. We find the surprising result that all 2-point functions of gauge currents fall into the same universality class, irrespectively of whether they correspond to broken or unbroken symmetries. We show that the problem of finding the spectrum can be mapped into an equivalent Schroedinger problem for supersymmetric quantum mechanics. The corresponding potential is the supersymmetric partner of the potential arising in studies of the spectrum for massless scalars and transverse graviton fluctuations in these backgrounds and the associated spectra are also identical. We discuss in detail two examples where these computations can be done explicitly as in the conformal case.

hep-th↗

arXiv2001

Gauge Theory at Large N and New G_2 Holonomy Metrics

We find a one-parameter family of new G_2 holonomy metrics and demonstrate that it can be extended to a two-parameter family. These metrics play an important role as the supergravity dual of the large $N$ limit of four dimensional supersymmetric Yang-Mills. We show that these G_2 holonomy metrics describe the M-theory lift of the supergravity solution describing a collection of D6-branes wrapping the supersymmetric three-cycle of the deformed conifold geometry for any value of the string coupling constant.

hep-th↗

arXiv1999

The D4-D8 Brane System and Five Dimensional Fixed Points

We construct dual Type I' string descriptions to five dimensional supersymmetric fixed points with $E_{N_f+1}$ global symmetry. The background is obtained as the near horizon geometry of the D4-D8 brane system in massive Type IIA supergravity. We use the dual description to deduce some properties of the fixed points.

hep-th↗

arXiv1999

Branes at Singularities in Type 0 String Theory

We consider Type 0B D3-branes placed at conical singularities and analyze in detail the conifold singularity. We study the non supersymmetric gauge theories on their worldvolume and their conjectured dual gravity descriptions. In the ultraviolet the solutions exhibit a logarithmic running of the gauge coupling. In the infrared we find confining solutions and IR fixed points.

hep-th↗

arXiv1999

Wilson Loops, Confinement, and Phase Transitions in Large N Gauge Theories from Supergravity

We use the recently proposed supergravity approach to large $N$ gauge theories to calculate ordinary and spatial Wilson loops of gauge theories in various dimensions. In this framework we observe an area law for spatial Wilson loops in four and five dimensional supersymmetric Yang-Mills at finite temperature. This can be interpreted as the area law of ordinary Wilson loops in three and four dimensional non-supersymmetric gauge theories at zero temperature which indicates confinement in these theories. Furthermore, we show that super Yang Mills theories with 16 supersymmetries at finite temperature do not admit phase transitions between the weakly coupled super Yang Mills and supergravity regimes. This result is derived by analyzing the entropy and specific heat of those systems as well as by computing ordinary Wilson loops at finite temperature. The calculation of the entropy was carried out in all different regimes and indicates that there is no first order phase transition in these systems. For the same theories at zero temperature we also compute the dependence of the quark anti-quark potential on the separating distance.

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