Showing 1 - 10 of 11 Items

Date: 2013-04-19

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are mostsubleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N = 8 supergravity and mostsubleading-color N = 4 SYM amplitudes that holds for the two leading IR divergences, (Formula presented.) and (Formula presented.), but breaks down at (Formula presented.).

Date: 2005-07-01

Creator: Marta Gómez-Reino, Stephen G. Naculich, Howard J. Schnitzer

Access: Open access

We extend the methods of Spradlin and Volovich to compute the partition function for a conformally-invariant gauge theory on ℝ × S 3 in which the dilatation operator is represented by a spin-chain hamiltonian acting on pairs of states, not necessarily nearest neighbors. A specific application of this is the two-loop dilatation operator of the planar SU(2) subsector of the N ≤ 4 SU(N) super Yang-Mills theory in the large-N limit. We compute the partition function and Hagedorn temperature for this sector to second order in the gauge coupling. The Hagedorn temperature is to be interpreted as giving the exponentially-rising portion of the density of states of the SU(2) sector, which may be a signal of stringy behavior in the dual theory. © SISSA 2005.

Date: 2003-01-01

Creator: Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Access: Open access

We use matrix model technology to study the N = 2 U (N) gauge theory with Nf massive hypennultiplets in the fundamental representation. We perform a completely perturbative calculation of the periods ai and the prepotential F(a) up to the first instanton level, finding agreement with previous results in the literature. We also derive the Seiberg-Witten curve and differential from the large-M solution of the matrix model. We show that the two cases Nf < N and N ≤ Nf < 2N can be treated simultaneously. © SISSA/ISAS 2003.

Date: 2004-04-01

Creator: Marta Gómez-Reino, Howard J. Schnitzer, Stephen G. Naculich

Access: Open access

We present a matrix-model expression for the sum of instanton contributions to the prepotential of an N = 2 supersymmetric U (N) gauge theory, with matter in various representations. This expression is derived by combining the renormalization-group approach to the gauge theory prepotential with matrix-model methods. This result can be evaluated order-by-order in matrix-model perturbation theory to obtain the instanton corrections to the prepotential. We also show, using this expression, that the one-instanton prepotential assumes a universal form. © SISSA/ISAS 2004.

Date: 2012-02-27

Creator: Stephen G. Naculich, Horatiu Nastase, Howard J. Schnitzer

Access: Open access

The IR divergences of supergravity amplitudes are less severe than those of planar SYM amplitudes, and are comparable to those subleading-color SYM amplitudes that are most subleading in the 1/N expansion, namely O(1/ε L) for L-loop amplitudes. We derive linear relations between one- and two-loop four-point amplitudes and one-loop five-point amplitudes of N ≥ 4, 5, and 6 supergravity and the most-subleading-color contributions of the analogous amplitudes of N = 0, 1, and 2 SYM theory, extending earlier results for N = 8 supergravity amplitudes. Our work relies on linear relations between N = 4 supergravity and planar SYM amplitudes that were recently derived using the double-copy property of gravity, and color-kinematic duality of gauge theories. © SISSA 2012.

Date: 2010-01-01

Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin

Access: Open access

We extend the analysis of Higgs-regulated planar amplitudes of N = 4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N = 4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n ≥ 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion. © 2010 SISSA, Trieste, Italy.

Date: 2003-08-01

Creator: Stephen G. Naculich, Howard J. Schnitzer, Niclas Wyllard

Access: Open access

We study the matrix model/gauge theory connection for three different N =1 models: U(N) × U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U (N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to establish the relation between the gauge theories and the matrix models. We find that the gauge coupling matrix for U (N) with matter in the symmetric or antisymmetric representations is not given by the second derivative of the matrix-model free energy. However, the matrix-model prescription can be modified to give the gauge coupling matrix. © SISSA/ISAS 2003.

Date: 2011-11-21

Creator: Stephen G. Naculich, Howard J. Schnitzer

Access: Open access

We derive a linear relation between the one-loop five-point amplitude of N = 8 supergravity and the one-loop five-point subleading-color amplitudes of N = 4 supersymmetric Yang-Mills theory. © 2011 SISSA.

Date: 2010-01-01

Creator: Johannes M. Henn, Stephen G. Naculich, Howard J. Schnitzer, Marcus Spradlin

Access: Open access

We compute the three-loop contribution to the N = 4 supersymmetric Yang- Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization. © SISSA 2010.

Date: 2009-11-11

Creator: Stephen G. Naculich, Howard J. Schnitzer

Access: Open access

We derive a compact all-loop-order expression for the IR-divergent part of the = 4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N 2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops. © SISSA 2009.