Showing 1 - 7 of 7 Items

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: 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: 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.