arXiv subjects
Publications and source records attributed to J. F. Morales.
In this paper we compute gaugino and scalar condensates in N=1 supersymmetric gauge theories with and without massive adjoint matter, using localization formulae over the multi--instanton moduli space. Furthermore we compute the chiral ring relations among the correlators of the $N=1^*$ theory and check this result against the multi-instanton computation finding agreement.
We derive the coherent state representation of the integrable spin chain Hamiltonian with non-compact supersymmetry group G=SU(1,1|1). By passing to the continuous limit, we find a spin chain sigma model describing a string moving on the supercoset G/H, H being the stabilizer group. The action is written in a manifestly G-invariant form in terms of the Cartan forms and the string coordinates in the supercoset. The spin chain sigma model is shown to agree with that following from the Green-Schwarz action describing two-charged string spinning on AdS_5 x S^5.
We derive the spectrum of gauge invariant operators for maximally supersymmetric Yang-Mills theories in d dimensions. After subtracting the tower of BPS multiplets, states are shown to fall into long multiplets of a hidden SO(10,2) symmetry dressed by thirty-two supercharges. Their primaries organize into a universal, i.e. d-independent pattern. The results are in perfect agreement with those following from (naive) KK reduction of type II strings on the warped AdS x S near-horizon geometry of Dp-branes.
We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL(2,R). By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL(2,R)/U(1). The same sigma model is found by considering strings rotating with large angular momentum in AdS_5xS^5. The spinning strings are identified with semiclassical coherent states built out of SL(2,R) spin chain states.
We review the spin bit model describing anomalous dimensions of the operators of Super Yang--Mills theory. We concentrate here on the scalar sector. In the limit of large $N$ this model coincides with integrable spin chain while at finite N it has nontrivial chain splitting and joining interaction.
We study spin models underlying the non-planar dynamics of ${\cal N}=4$ SYM gauge theory. In particular, we derive the non-local spin chain Hamiltonian generating dilatations in the gauge theory at leading order in $g_{\rm YM}^2 N$ but exact in ${1\over N}$. States in the spin chain are characterized by a spin-configuration and a linking variable describing how sites in the chain are connected. Joining and splitting of string/traces are mimicked by a twist operator acting on the linking variable. The results are applied to a systematic study of non-planar anomalous dimensions and operator mixing in ${\cal N}=4$ SYM. Intriguingly, we identify a sequence of SYM operators for which corrections to the one-loop anomalous dimensions stop at the first ${1\over N}$ non-planar order.
The prepotential in N=2 SUSY Yang-Mills theories enjoys remarkable properties. One of the most interesting is its relation to the coordinate on the quantum moduli space $u=< \tr ϕ^2>$ that results into recursion equations for the coefficients of the prepotential due to instantons. In this work we show, with an explicit multi-instanton computation, that this relation holds true at arbitrary winding numbers. Even more interestingly we show that its validity extends to the case in which gravitational corrections are taken into account if the correlators are suitably modified. These results apply also to the cases in which matter in the fundamental and in the adjoint is included. We also check that the expressions we find satisfy the chiral ring relations for the gauge case and compute the first gravitational correction.
We test the spectrum of string theory on AdS_5 x S^5 derived in hep-th/0305052 against that of single-trace gauge invariant operators in free N=4 super Yang-Mills theory. Masses of string excitations at critical tension are derived by extrapolating plane-wave frequencies at g_{YM}=0 down to finite J. On the SYM side, we present a systematic description of the spectrum of single-trace operators and its reduction to PSU(2,2|4) superconformal primaries via a refined Eratostenes' supersieve. We perform the comparison of the resulting SYM/string spectra of charges and multiplicities order by order in the conformal dimension Δup to Δ=10 and find perfect agreement. Interestingly, the SYM/string massive spectrum exhibits a hidden symmetry structure larger than expected, with bosonic subgroup SO(10,2) and thirty-two supercharges.
We discuss spectra of $AdS_3$ supergravities, arising in the near horizon geometry of D1/D5 systems in orbifolds/orientifolds of type IIB theory with 16 supercharges. These include models studied in a recent paper (hep-th/0012118), where the group action involves also a shift along a transversal circle, as well as IIB/$ΩI_4$, which is dual to IIB on $K3$. After appropriate assignements of the orbifold group eigenvalues and degrees to the supergravity single particle spectrum, we compute the supergravity elliptic genus and find agreement, in the expected regime of validity, with the elliptic genus obtained using U-duality map from (4,4) CFTs of U-dual backgrounds. Since this U-duality involves the exchange of KK momentum $P$ and D1 charge $N$, it allows us to test the (4,4) CFTs in the $P < N/4$ and $N < P/4$ regimes by two different supergravity duals.
We propose CFT descriptions of the D1/D5 system in a class of freely acting Z_2 orbifolds/orientifolds of type IIB theory, with sixteen unbroken supercharges. The CFTs describing D1/D5 systems involve N=(4,4) or N=(4,0) sigma models on $(R^3\times S^1\times T^4\times (T^4)^N/S_N)/Z_2$, where the action of Z_2 is diagonal and its precise nature depends on the model. We also discuss D1(D5)-brane states carrying non-trivial Kaluza-Klein charges. The resulting multiplicities for two-charge bound states are shown to agree with the predictions of U-duality. We raise a puzzle concerning the multiplicities of three-charge systems, which is generically present in all vacuum configurations with sixteen unbroken supercharges studied so far, including the more familiar type IIB on K3 case: the constraints put on BPS counting formulae by U-duality are apparently in contradiction with any CFT interpretation. We argue that the presence of RR backgrounds appearing in the symmetric product CFT may provide a resolution of this puzzle.
We determine the spectrum of D-string bound states in various classes of generalized type I vacuum configurations with sixteen and eight supercharges. The precise matching of the BPS spectra confirms the duality between unconventional type IIB orientifolds with quantized NS-NS antisymmetric tensor and heterotic CHL models in D=8. A similar analysis puts the duality between type II (4,0) models and type I strings {\it without open strings} on a firmer ground. The analysis can be extended to type II (2,0) asymmetric orbifolds and their type I duals that correspond to unconventional K3 compactifications. Finally we discuss BPS-saturated threshold corrections to the correponding low-energy effective lagrangians. In particular we show how the exact moduli dependence of some F^4 terms in the eight-dimensional type II (4,0) orbifold is reproduced by the infinite sum of D-instanton contributions in the dual type I theory.
We study ${\cal F}^4$-threshold corrections in an eight dimensional S-dual pair of string theories, as a prototype of dual string vacua with sixteen supercharges. We show that the orbifold CFT description of D-string instantons gives rise to a perturbative expansion similar to the one appearing on the fundamental string side. By an explicit calculation, using the Nambu-Goto action in the static gauge, we show that the first subleading term agrees precisely on the two sides. We then give a general argument to show that the agreement extends to all orders.
Spin interactions beteween two moving Dp-branes are analyzed using the Green-Schwarz formalism of boundary states. This approach turns out to be extremely efficient to compute all the spin effects related by supersymmetry to the leading v^4/r^7-p term. All these terms are shown to be scale invariant, supporting a matrix model description of supergravity interactions. By employing the LSZ reduction formula for matrix theory and the mentioned supersymmetric effective potential for D0-branes, we compute the t-pole of graviton-graviton and three form-three form scattering in matrix theory. The results are found to be in complete agreement with tree level supergravity in the corresponding kinematical regime and provide, moreover, an explicit map between these degrees of freedom in both theories.
We study the infra-red limit of the O(N) gauge theory that describes the low energy modes of a system of $N$ type I D-strings and provide some support to the conjecture that, in this limit, the theory flows to an orbifold conformal theory. We compute the elliptic genus of the orbifold theory and argue that its longest string sector describes the bound states of D-strings. We show that, as a result, the masses and multiplicities of the bound states are in agreement with the predictions of heterotic-type I duality in 9 dimensions, for all the BPS charges in the lattice $Γ_{(1,17)}$.
We study the spin dependence of D-brane dynamics in the Green-Schwarz formalism of boundary states. In particular we show how to interpret insertion of supercharges on the boundary state as sources of non-universal spin effects in D-brane potentials. In this way we find for a generic (D)p-brane, potentials going like $v^{4-n}/r^{7-p+n}$ corresponding to interactions between the different components of the D-brane supermultiplet. From the eleven dimensional point of view, these potentials arise from the exchange of field strengths corresponding to the graviton and the three form, coupled non-minimally to the branes. We show how an annulus computation truncated to its massless contribution is enough to reproduce these next-to-leading effects, meaning in particular that the one-loop (M)atrix theory effective action should encode all the spin dependence of low-energy supergravity interactions.