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There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are chosen in a specific way, by showing that they can both be reduced to the same integral over a moduli space of singular curves. We also formulate a class of new ``intermediate prescriptions to calculate the same amplitudes.
We consider the twistor space ${cal P}^6cong{mathbb R}^4{times}{mathbb C}P^1$ of ${mathbb R}^4$ with a non-integrable almost complex structure ${cal J}$ such that the canonical bundle of the almost complex manifold $({cal P}^6, {cal J})$ is trivial.
We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides
We give a unified division algebraic description of (D=3, N=1,2,4,8), (D=4, N=1,2,4), (D=6, N=1,2) and (D=10, N=1) super Yang-Mills theories. A given (D=n+2, N) theory is completely specified by selecting a pair (A_n, A_{nN}) of division algebras, A_
We show how to consistently renormalize $mathcal{N} = 1$ and $mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportio
We construct the 4-dimensional ${cal N}=frac12$ and ${cal N}=1$ inhomogeneously mass-deformed super Yang-Mills theories from the ${cal N} =1^*$ and ${cal N} =2^*$ theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is at