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I-odd sector of the Klebanov-Strassler theory

Anatoly Dymarsky, Dmitry Melnikov, Alexander Solovyov

TL;DR

This work completes the holographic spectrum of I-odd SU(2)×SU(2) singlet fluctuations around the Klebanov-Strassler background by identifying three spin-0 and seven spin-1 bosonic modes that organize into Vector Multiplet I and Gravitino Multiplets II and IV in the KW framework. The authors construct a general I-odd ansatz using T^{1,1} invariant forms, derive and diagonalize coupled linear equations for the spin-1 fluctuations, and extract two $${j=1}$$ multiplets with vector ${X}_{\pm}$ and axial ${Y}_{\pm}$, alongside the Betti-vector mix. They compute the glueball spectra numerically, obtaining the lightest masses $${\tilde{m}}^2_{-} = 1.78$$ and $${\tilde{m}}^2_{+} = 2.83$$ and fit higher levels, while discussing scaling-dimension mixing via Supersymmetric Quantum Mechanics and dual operators in the N=1 SYM sector. The results illuminate how KS departs from conformality by mixing NS-NS and RR sectors and by linking to pure-gauge operators, offering a bridge to understanding YM-like dynamics in a holographic setup and suggesting extensions to the I-even sector.

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.

I-odd sector of the Klebanov-Strassler theory

TL;DR

This work completes the holographic spectrum of I-odd SU(2)×SU(2) singlet fluctuations around the Klebanov-Strassler background by identifying three spin-0 and seven spin-1 bosonic modes that organize into Vector Multiplet I and Gravitino Multiplets II and IV in the KW framework. The authors construct a general I-odd ansatz using T^{1,1} invariant forms, derive and diagonalize coupled linear equations for the spin-1 fluctuations, and extract two multiplets with vector and axial , alongside the Betti-vector mix. They compute the glueball spectra numerically, obtaining the lightest masses and and fit higher levels, while discussing scaling-dimension mixing via Supersymmetric Quantum Mechanics and dual operators in the N=1 SYM sector. The results illuminate how KS departs from conformality by mixing NS-NS and RR sectors and by linking to pure-gauge operators, offering a bridge to understanding YM-like dynamics in a holographic setup and suggesting extensions to the I-even sector.

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.

Paper Structure

This paper contains 20 sections, 95 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. $\mathcal{I}$-odd excitations over the KS background
  3. General ansatz
  4. Supermultiplet structure in the conformal case
  5. Triplet of vectors from the Gravitino Multiplets
  6. Derivation of the equations
  7. Analysis of the equations
  8. Betti vector and axial vector triplet
  9. Derivation of the equations
  10. Analysis of the equations
  11. Analysis of the results
  12. Numerical calculation of spectra
  13. Scaling dimensions and SQM
  14. Operators of the dual gauge theory
  15. Discussion and final remarks
  16. ...and 5 more sections

Figures (2)

  • Figure 1: Values of $\tilde{m}^2$ and $J^{PC}$ quantum numbers of the states from the $\mathrm{SU}(2)\times \mathrm{SU}(2)$ invariant $\mathcal{I}$-odd sector. Each infinite tower is represented by it's lightest massive mode. Also in the figure: the massless scalar multiplet and the lightest states of the $\mathcal{I}$-even Graviton multiplet $1^{++},2^{++}$.
  • Figure 2: (a) Pure gauge sector of the KS theory. Conjectured positions of $0^{++}$ and $0^{-+}$ states are marked by dashed lines. (b) Spectrum of non-supersymmetric pure glue $\mathrm{SU}(3)$ theory Morningstar. Both spectra are normalized to the mass of $2^{++}$ state.