arXiv subjects
Publications and source records attributed to Freddy Cachazo.
We analyze the twistor space structure of certain one-loop amplitudes in gauge theory. For some amplitudes, we find decompositions that make the twistor structure manifest; for others, we explore the twistor space structure by finding differential equations that the amplitudes obey.
We show that, in analyzing differential equations obeyed by one-loop gauge theory amplitudes, one must take into account a certain holomorphic anomaly. When this is done, the results are consistent with the simplest twistor-space picture of the available one-loop amplitudes.
As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued off shell in a particular fashion. The formalism leads to new and relatively simple formulas for many amplitudes, and can be heuristically derived from twistor space.
We study supersymmetric Sp(N) gauge theories with an antisymmetric tensor and degree n+1 tree level superpotential. The generalized Konishi anomaly equations derived in hep-th/0304119 and hep-th/0304138 are used to compute the low energy superpotential of the theory. This is done by imposing a certain integrality condition on the periods of a meromorphic one form. Explicit computations for Sp(2), Sp(4), Sp(6) and Sp(8) with cubic superpotential are done and full agreement with the results of the dynamically generated superpotential approach is found. As a byproduct, we find a very precise map from Sp(N) to a U(N+2n) theory with one adjoint and a degree n+1 tree level superpotential.
We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected.
N=1 supersymmetric U(N) gauge theory with adjoint matter $Φ$ and a polynomial superpotential $\Tr W(Φ)$ has been much studied recently. The classical theory has several vacua labeled by integers $(N_1,N_2,...,N_k)$, with the classical unbroken gauge group $\prod_i U(N_i)$. Quantum mechanically, each classical vacuum leads to $\prod_i N_i$ different vacua. As the parameters of $W(Φ)$ are varied, these vacua change in a continuous (and holomorphic) fashion. We find that vacua associated with $(N_1,N_2,...,N_k)$ can be continuously transformed to vacua with $(\tilde N_1,\tilde N_2,...,\tilde N_k)$, thus leading to a new kind of duality. Traditional order parameters, like the Wilson loop and 't Hooft loop, sometimes distinguish different phases. We also find phases that are not distinguished by conventional order parameters. The whole picture of the phase diagram is reminiscent of the phase diagram of $M$-theory.
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of ``integration constants.'' From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of $\N=1$ super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate.
We provide a proof of the equivalence of N=1 dynamics obtained by deforming N=2 supersymmetric gauge theories by addition of certain superpotential terms, with that of type IIB superstring on Calabi-Yau threefold geometries with fluxes. In particular we show that minimization of the superpotential involving gaugino fields is equivalent to finding loci where Seiberg-Witten curve has certain factorization property. Moreover, by considering the limit of turning off of the superpotential we obtain the full low energy dynamics of N=2 gauge systems from Calabi-Yau geometries with fluxes.