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

147

207

We consider classical strings propagating in a background generated by a sequence of TsT transformations. We describe a general procedure to derive the Green-Schwarz action for strings. We show that the U(1) isometry variables of the TsT-transformed background are related to the isometry variables of the initial background in a universal way independent of the details of the background. This allows us to prove that strings in the TsT-transformed background are described by the Green-Schwarz action for strings in the initial background subject to twisted boundary conditions. Our construction implies that a TsT transformation preserves integrability properties of the string sigma model. We discuss in detail type IIB strings propagating in the γ i -deformed AdS 5 ×S 5 space-time, find the twisted boundary conditions for bosons and fermions, and use them to write down an explicit expression for the monodromy matrix. We also discuss string zero modes whose dynamics is governed by a fermionic generalization of the integrable Neumann model. *

mentioning

confidence: 99%

Green-Schwarz Strings in TsT-transformed backgrounds

Alday¹,

Arutyunov²,

Frolov³

2006

147

207

“…so that we make the replacement l → 2l. Now 12 Since e −2Φ √ G is, in general, invariant under T-duality and G tt is not affected by the T-dualities we performed. 13 If we make a general ansatz of the form Ψ ⊥ ∼ e iniφi ψ (1) (ψ, θ)ψ (2) (r), where n i ∈ Z, the modification of the differential equation depends on the matrix λ ij in (6.2) via a term of the form −γ 2 λ ij n i n j .…”

Section: The Deformed Casementioning

confidence: 99%

Gravity duals for the Coulomb branch of marginally deformed Script N = 4 Yang-Mills

Hernández

Sfetsos

Zoakos

2006

Supergravity backgrounds dual to a class of exactly marginal deformations of N = 4 supersymmetric Yang-Mills can be constructed through an SL(2, R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N = 1 theories at strong 't Hooft coupling as marginal deformations of N = 4 Yang-Mills. For concreteness we concentrate to cases with an SO(4) × SO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitations on these backgrounds are analyzed by turning the associated differential equations into Schrödinger problems. We find explicit solutions taking into account the entire tower of states related to the reduction of type-IIB supergravity to five dimensions, and hence we go beyond the s-wave approximation that has been considered before for the undeformed case. Arbitrary values of the deformation parameter give rise to the Heun differential equation and the related Inozemtsev integrable system, via a non-standard trigonometric limit as we explicitly demonstrate.

“…This deformation is called as a β deformation. Some aspects of more general three-parameter deformed AdS 5 × S 5 and the dual nonsupersymmetric deformations of N = 4 SYM have been studied in papers [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. It is unclear, however, if the non-supersymmetric string background is stable.…”

Section: Introductionmentioning

confidence: 99%

“…It is unclear, however, if the non-supersymmetric string background is stable. For example, it is known that the spectrum of string theory in the TsT-transformed flat space contains tachyon [28]. However it does not imply that string theory on the deformed AdS 5 × S 5 is unstable because the TsT-transformed flat space is singular at space infinity while the deformed AdS 5 × S 5 is regular everywhere.…”

Section: Introductionmentioning

confidence: 99%

Pure spinor strings in TsT deformed background

Grassi

Klusoň

2007

We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermionic variables we can construct pure spinor action with manifest U(1) isometry. This fact implies that the pure spinor string in TsT-transformed background is described by pure spinor string in the original background where world-volume modes are subject to twisted boundary conditions. We will argue that these twisted boundary conditions generally prevent to prove the quantum conformal invariance of the pure spinor string in AdS 5 × S 5 background. We determine the conditions under which this quantum conformal invariance can be proved. We also determine the Lax pair for pure spinor strings in the TsT-transformed background.