ℐ-odd sector of the Klebanov-Strassler theory

Abstract

The Klebanov-Strassler background is invariant under the Z 2 symmetry I, which acts by exchanging the bi-fundamental fields A and B, accompanied by the charge conjugation. We study the background perturbations in the I-odd sector and find an exhaustive list of bosonic states invariant under the global SU(2)×SU(2) symmetry. In addition to the scalars identified in an earlier publication arXiv: 0712.4404 we find 7 families of massive states of spin 1. Together with the spin 0 states they form 3 families of massive vector multiplets and 2 families of massive gravitino multiplets, containing a vector, a pseudovector and fermions of spin 3/2 and 1/2. In the conformal Klebanov-Witten case these I-odd particles belong to the N = 1 superconformal Vector Multiplet I and Gravitino Multiplets II and IV. The operators dual to the I-odd singlet sector include those without bi-fundamental fields making an interesting connection with the pure N = 1 SYM theory. We calculate the mass spectrum of the corresponding glueballs numerically and discuss possible applications of our results. * Now at Tel Aviv University, Ramat Aviv 69978, IsraelThe Klebanov-Strassler supergravity solution, which corresponds to a certain vacuum of the SU(k(M + 1)) × SU(kM) gauge theory [1], provides an interesting and rich example of the gauge/string duality [2,3,4]. It generalizes the duality between the superconformal SU(N) × SU(N) gauge theory with bi-fundamentals and string theory on AdS 5 × T 1,1 [5].Adding extra colors to one of the gauge groups breaks the conformal symmetry [6,7,8] and leads to the cascade behavior [1,9,10]. The gauge group SU(k(M + 1)) × SU(kM) shrinks to SU(M) at the bottom of the cascade and the KS theory reduces to the pure gauge N = 1 SYM [1]. Unfortunately such a limit requires small g s M, which makes the supergravity approximation invalid. Nevertheless this connection between the KS solution and the pure super-Yang-Mills theory strongly motivates the studies of the bifundamental free sector of the SU(k(M +1))×SU(kM) theory that survives at the bottom of the cascade. The KS solution is invariant under the Z 2 symmetry I, which acts by exchanging the two two-spheres of the deformed conifold accompanied by the inversion of sign of the 3-form flux. On the field theory side this symmetry exchanges and conjugates the bi-fundamental fields A and B. Thus the KS solution corresponds to one particular Iinvariant vacuum |A| 2 = |B| 2 . The latter spontaneously breaks U(1) Baryon symmetry A → Ae ia , B → Be −ia . The corresponding massless Goldstone pseudoscalar a combines with the scalar U ∼ |A| 2 − |B| 2 into a I-odd scalar supermultiplet [11]. While a corresponds to the longitudinal part of the U(1) Baryon current J µ = ∂ µ a, the fluctuation of U changes the expectation values of the baryon operators A, B and moves the theory along the baryonic branch of the moduli space [11,12,13,14].The massless I-odd supermultiplet (U, a) was first studied in [11]. Later this analysis was generalized to the massive excitations in [15]. In partic...

Valence quark contributions for the γ*N→N(1440) form factors from light-front holography

“…A prototypical example would be (the glueball sector of) the Klebanov-Strassler theory [64,81]. Albeit supersymmetric, this theory encodes a logarithmically running gauge coupling, thus, extracting dimensions of the operators in this theory requires removing the logarithmic scale dependence (e.g., [82][83][84]). Moreover, in this theory, the states with the same quantum numbers tend to mix with each other.…”

“…Therefore the mass eigenstates are superpositions of states with different twist. Mixing has effect of changing the resulting spectrum as well as shifting the values of the dimensions [83][84][85][86][87].…”

Glueballs on the baryonic branch of Klebanov-Strassler: dimensional deconstruction and a light scalar particle

“…We will explicitly check that in the two appropriate limits our results reproduce the known ones for the KS and CVMN case. Namely, in the KS case it is known that the spectrum is discrete, and has been studied in detail [12,[49][50][51][52][53][54][55], while in the CVMN case the spectrum has no discrete (bound) states, but exhibits a mass gap, beyond which a continuum appears [11]. The latter is a manifestation of the fact that at energies far above the confinement scale the field theory described by the CVMN system is six dimensional, as is apparent in gravity from the fact that the internal S 2 is blowing up towards the UV.…”

“…We focus on the large class of backgrounds that lifts to the whole baryonic branch of the KS system [28] -as well as its extrema corresponding to the CVMN [23,24] and KS [22] solutions. In the literature of conifold backgrounds, some important features have been discussed for example in [29,[45][46][47][48], but the full detailed gravity calculations at strong (field theory) coupling exist only for the KS solution [11,12,[49][50][51][52][53][54][55] and the CVMN solution [11,12].…”

Supersymmetric consistent truncations of IIB on T 1,1

“…A thorough understanding of these deformations is important for many problems in string cosmology and phenomenology and there has been much work on computing the spectrum of fluctuations around KS (for example [13][14][15][16][17][18]) but to our knowledge certain SU(2) × SU(2) invariant modes which lie within our ansatz have not been considered. These modes are crucial for constructing a supersymmetric five-dimensional theory and thus are needed to arrange the spectrum into supermultiplets.…”