Showing 1 - 9 of 9 Items

More pendants for Polya: Two loops in the SU(2) sector

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.

Matrix model approach to the N = 2 U (N) gauge theory with matter in the fundamental representation

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.

Improved matrix-model calculation of the N = 2 prepotential

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.

Linear relations between N ≥ 4 supergravity and subleading-color SYM amplitudes

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.

Cubic curves from matrix models and generalized Konishi anomalies

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.

One-loop SYM-supergravity relation for five-point amplitudes

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.

A tale of two exponentiations in N = 8 supergravity at subleading level

Date: 2020-03-01

Creator: Paolo Di Vecchia, Stephen G. Naculich, Rodolfo Russo, Gabriele Veneziano, Chris D., White

Access: Open access

High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in ϵ, hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM theory

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.

All-loop-orders relation between Regge limits of N = 4 SYM and N = 8 supergravity four-point amplitudes

Date: 2021-02-01

Creator: Stephen G. Naculich

Access: Open access

We examine in detail the structure of the Regge limit of the (nonplanar) N = 4 SYM four-point amplitude. We begin by developing a basis of color factors Cik suitable for the Regge limit of the amplitude at any loop order, and then calculate explicitly the coefficients of the amplitude in that basis through three-loop order using the Regge limit of the full amplitude previously calculated by Henn and Mistlberger. We compute these coefficients exactly at one loop, through O(ϵ 2) at two loops, and through O(ϵ) at three loops, verifying that the IR-divergent pieces are consistent with (the Regge limit of) the expected infrared divergence structure, including a contribution from the three-loop correction to the dipole formula. We also verify consistency with the IR-finite NLL and NNLL predictions of Caron-Huot et al. Finally we use these results to motivate the conjecture of an all-orders relation between one of the coefficients and the Regge limit of the N = 8 supergravity four-point amplitude.