Radu Roiban

Beauty and the twist: the Bethe ansatz for twisted Script N = 4 SYM

It was recently shown that the string theory duals of certain deformations of the = 4 gauge theory can be obtained by a combination of T-duality transformations and coordinate shifts. Here we work out the corresponding procedure of twisting the dual integrable spin chain and its Bethe ansatz. We derive the Bethe equations for the complete twisted = 4 gauge theory at one and higher loops. These have a natural generalization which we identify as twists involving the Cartan generators of the conformal algebra. The underlying model appears to be a form of noncommutative deformation of = 4 SYM.

Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory

We consider a nonsupersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS5 × S 5 by a combination of T-dualities and shifts of angular coordinates. It depends on three real parameters γi which determine the shape of the deformed 5-sphere. The dual gauge theory has the same field content as N = 4 SYM theory, but with scalar and Yukawa interactions “deformed” by γi -dependent phases. The special case of equal γi = γ corresponds to the N = 1 supersymmetric deformation. We compare the energies of semiclassical strings with three large angular momenta to the 1-loop anomalous dimensions of the corresponding gauge-theory scalar operators and find that they match as it was the case in the SU(3) sector of the standard AdS/CFT duality. In the supersymmetric case of equal γi this extends the result of our previous work (hep-th/0503192) from the 2-spin to the 3-spin sector. This extension turns out to be quite nontrivial. To match the corresponding low-energy effective “Landau– Lifshitz” actions on the string theory and the gauge theory sides one is to make a special choice of the spin chain Hamiltonian representing the 1-loop gauge theory dilatation operator. This choice is adapted to low-energy approximation, i.e., it allows one to capture the right vacuum states and the “macroscopic spin wave” sector of states of the spin chain in the continuum coherent state effective action.  2005 Elsevier B.V. All rights reserved.

A googly amplitude from the B-model in twistor space

Recently it has been proposed that gluon scattering amplitudes in gauge theory can be computed from the D-instanton expansion of the topological B-model on 3|4, although only maximally helicity violating (MHV) amplitudes have so far been obtained from a direct B-model calculation. In this note we compute the simplest non-MHV gluon amplitudes (+ + - - - and + - + - -) from the B-model as an integral over the moduli space of degree 2 curves in 3|4 and find perfect agreement with Yang-Mills theory.

On spin chains and field theories

We point out that the existence of global symmetries in a fleld theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a fleld theory whose 1-loop scale transformations are generated by the spin chain hamiltonian. We also identify a necessary condition for a given fleld theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated fleld theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the intro- duction of more propagating bosonic flelds. For the case of a 2-state chain we flnd the spectrum and the eigenstates. For certain values of its coupling constants the fleld theory associated to this general type of chain is the bosonic sector of the q-deformation ofN = 4 SYM theory.

Yang-Mills correlation functions from integrable spin chains

The relation between the dilatation operator of = 4 Yang-Mills theory and integrable spin chains makes it possible to compute the one-loop anomalous dimensions of all operators in the theory. In this paper we show how to apply the technology of integrable spin chains to the calculation of Yang-Mills correlation functions by expressing them in terms of matrix elements of spin operators on the corresponding spin chain. We illustrate this method with several examples in the SU(2) sector described by the XXX1/2 chain.

Supergravity pp -wave solutions with 28 and 24 supercharges

We conduct an exhaustive search for solutions of IIA and IIB supergravity with augmented supersymmetry. We find a two-parameter family of IIB solutions preserving 28 supercharges, as well as several other IIA and IIB families of solutions with 24 supercharges. Given the simplicity of the pp-wave solution, the algorithm described here represents a systematic way of classifying all such solutions with augmented supersymmetry. By T-dualizing some of these solutions we obtain exact non-pp wave supergravity solutions (with 8 or 16 supercharges), which can be interpreted as perturbations of the AdS-CFT correspondence with irrelevant operators.

Perturbative gauge theory and closed string tachyons

We find an interesting connection between perturbative large N gauge theory and closed superstrings. The gauge theory in question is found on N D3-branes placed at the tip of the cone 6/Γ. In our previous work we showed that, when the orbifold group Γ breaks all supersymmetry, then typically the gauge theory is not conformal because of double-trace couplings whose one-loop beta functions do not possess real zeros. In this paper we observe a precise correspondence between the instabilities caused by the flow of these double-trace couplings and the presence of tachyons in the twisted sectors of type IIB theory on orbifolds 3,1 × 6/Γ. For each twisted sectors that does not contain tachyons, we show that the corresponding double-trace coupling flows to a fixed point and does not cause an instability. However, whenever a twisted sector is tachyonic, we find that the corresponding one-loop beta function does not have a real zero, hence an instability is likely to exist in the gauge theory. We demonstrate explicitly the one-to-one correspondence between the regions of stability/instability in the space of charges under Γ that arise in the perturbative gauge theory and in the free string theory. Possible implications of this remarkably simple gauge/string correspondence are discussed.

Perturbative search for fixed lines in large-N gauge theories

The logarithmic running of marginal double-trace operators is a general feature of 4-d field theories containing scalar fields in the adjoint or bifundamental representation. Such operators provide leading contributions in the large-N limit; therefore, the leading terms in their beta functions must vanish for a theory to be large-N conformal. We calculate the one-loop beta functions in orbifolds of the = 4 SYM theory by a discrete subgroup ? of the SU(4) R-symmetry, which are dual to string theory on AdS5 ? S5/?. We present a general strategy for determining whether there is a fixed line passing through the origin of the coupling constant space. Then we study in detail some classes of non-supersymmetric orbifold theories. Among our examples, which include orbifolds acting freely on the S5, we do not find any large-N non-supersymmetric theories with fixed lines passing through the origin. Connection of these results with closed string tachyon condensation in AdS5 ? S5/? is discussed.

Tree-level S matrix of Yang-Mills theory

In this note we further investigate the procedure for computing tree-level amplitudes in Yang-Mills theory from connected instantons in the B-model on P^{3|4}, emphasizing that the problem of calculating Feynman diagrams is recast into the problem of finding solutions to a certain set of algebraic equations. We show that the B-model correctly reproduces all 6-particle amplitudes, including non-MHV amplitudes with three negative and three positive helicity gluons. As a further check, we also show that n-particle amplitudes obtained from the B-model obey a number of properties required of gauge theory, such as parity symmetry (which relates an integral over degree d curves to one over degree n-d-2 curves) and the soft and collinear gluon poles.

Exact superpotentials in N = 1 theories with flavor and their matrix model formulation

Abstract In this Letter we investigate the effective superpotential of an N =1 U ( N c ) gauge theory with one adjoint chiral multiplet and N f fundamental chiral multiplets. We propose a matrix model prescription in which only matrix model diagrams with less than two boundaries contribute to the gauge theory effective superpotential. This prescription reproduces exactly the known gauge theory physics for all N f and N c . For N f ⩽ N c −1 this is given by the Affleck–Dine–Seiberg superpotential. For N f ⩾ N c +1 we present arguments leading to the conclusion that the dynamics of these theories is also reproduced by the matrix model.