MHV One-Loop Amplitudes in Yang-Mills from Generalised Unitarity

In this letter, we exploit generalised unitarity in order to calculate the cut-constructible part of one-loop amplitudes in non-supersymmetric Yang-Mills theory. In particular, we rederive the n-gluon MHV amplitudes for both the adjacent and non-adjacent gluon helicity configurations from 3- and 4-particle cuts alone.Comment: 20 pages, 4 figures; v3 version published in JHE

Beyond Logarithmic Corrections to Cardy Formula

As shown by Cardy modular invariance of the partition function of a given unitary non-singular 2d CFT with left and right central charges c_L and c_R, implies that the density of states in a microcanonical ensemble, at excitations Delta and Delta-bar and in the saddle point approximation, is \rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R \exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this paper, we extend Cardy's analysis and show that in the saddle point approximation and up to contributions which are exponentially suppressed compared to the leading Cardy's result, the density of states takes the form \rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta) f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R) is the product of contributions of left and right movers and hence, to this approximation, the partition function of any modular invariant, non-singular unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta; c_L, c_R)/(c_Lc_R) is only a function of $c_R\bar\Delta$ and $c_L\Delta$. In addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states of a microcanonical ensemble, we compute the entropy of the system in the canonical counterpart and show that the function f(x) is such that the canonical entropy, up to exponentially suppressed contributions, is simply given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added, v3: minor corrections to match the published versio

Unitarity Methods for Scattering Amplitudes in Perturbative Gauge Theories

EThOS - Electronic Theses Online ServiceGBUnited Kingdo