Exactly marginal operators and duality in four dimensional N = 1 supersymmetric gauge theory

All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk" del Pezzo models exist.

Section: Jhep04(2006)032mentioning

confidence: 89%

New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

“…For completeness, we note that P(β) satisfies the differential equation 9) where the coefficients depend only on τ 0 ,…”

Section: Metric and Form-fieldsmentioning

confidence: 99%

“…9 Furthermore, Lunin and Maldacena have demonstrated [2] that their supergravity solution with rational values of the β parameter is also related to the orbifold description via an action of the SL(2, Z) T-duality. Our solution agrees with that of Lunin-Maldacena for small β and hence its connection with the orbifold is guaranteed in this limit.…”

Section: Metric and Form-fieldsmentioning

confidence: 99%

“…Marginal deformations of the SYM have also been studied extensively in [9][10][11][12][13]. More recently, several perturbative calculations in the β-deformed theories were carried out in [14][15][16] where it was noted that there are many similarities between the deformed and the undeformed theories which emerge in perturbation theory in the large number of colours limit.…”

Section: Introductionmentioning

confidence: 99%

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String theory dual of the β-deformed gauge theory

Chu

Khoze

2006

We consider the AdS/CFT correspondence between the β-deformed supersymmetric gauge theory and the type IIB string theory on the Lunin-Maldacena background. Guided by gauge theory results, we modify and extend the supergravity solution of Lunin and Maldacena in two ways. First we make it to be doubly periodic in the deformation parameter, β → β + 1 and β → β + τ 0 , to match the β-periodicity property of the dual gauge theory. Secondly, we reconcile the SL(2, Z) symmetry of the gauge theory, which acts on the constant parameters τ 0 and β, with the SL(2, Z) invariance of the string theory, which involves the dilaton-axion field τ (x). Our proposed modified configuration transforms correctly under the SL(2, Z) of string theory when its parameters are transformed under the SL(2, Z) of the gauge theory. We interpret the resulting configuration as the string theory (rather than supergravity) background which is dual to the β-deformed conformal Yang-Mills. Finally, we check that our string theory background leads to the IIB effective action which is correctly reproduced by instanton calculations on the gauge theory side, carried out at weak coupling, in the large-N limit, but to all orders in the deformation parameter β.

“…Theory to a N = 1 superconformal gauge theory [13] (some recent interesting works on the (AdS 5 × S 5 ) β string theory can be found in [14 -25]). The Lunin-Maldacena deformation applies to the S 5 part of the space.…”

Section: Jhep09(2005)031mentioning

confidence: 99%

String spectrum of curved string backgrounds obtained by T-duality and shifts of polar angles

Russo

2005

A class of exactly solvable string models can be obtained by starting with flat space and combining T-duality and shifts of angular coordinates of several polar planes. The models are the analog of the Lunin-Maldacena β-deformation of the AdS 5 × S 5 type IIB string background, which is dual to a Leigh-Strassler deformation of N = 4 Super Yang-Mills Theory. We determine the complete physical string spectrum for two string models obtained in this way, by explicitly solving the string equations and quantizing in terms of free creation and annihilation operators. We also show that the 3-parameter (b 1 , b 2 , b 3 ) model, obtained by three independent TsT transformations, has tachyons in some regions of the parameter space.