Giant gravitons in m-deformed backgrounds

1
Giant gravitons in m-deformed backgrounds

• R. de Mello Koch, Norman Ives, Jelena Smolic,
  Milena Smolic
• hep-th/0509007

2
Introduction

• Want experimental data for string theories
• High energy experiments described by Yang-Mill
  gauge theories
• The AdS/CFT conjecture connection between
  string theories and field theories
• Type IIB string theory on AdS5S5
• equivalent to
• supersymmetric Yang-Mills on 4d Minkowski space
• Not quite good enough

3
Introduction

• No field theory which currently describes
  observed phenomena exhibits supersymmetry
• Necessary to find string theories dual to
  non-SUSY field theories
• QCD could be solved at low energy if the string
  theory dual were found
• Then wed have plenty of data

4
Initial steps

• Lunin and Maldacena showed how to find string
  theories dual to particular deformations of SYM
  (hep-th/0502086)
• Frolov generalised this deformation to break all
  the SUSY (hep-th/0503201)
• Frolov, Tseytlin and Roiban showed that the
  duality holds for rotating closed strings
  (hep-th/0507021)

5
Old favourites

• Along the way, FRT discovered a set of BPS
  objects in the non-SUSY background
• These are objects with charge equal to energy and
  in the SUSY setting are protected from quantum
  corrections.
• The most famous example of a BPS object is a
  giant graviton, and there is a wealth of slick
  machinery for dealing with them

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What is a giant graviton?

• In our case, an S3 moving in a plane in the S5
  part of the string theory background
• In the semi-classical limit, it has an equivalent
  description as a boundary condition for open
  string endpoints
• Couples to 5-form flux in such a way that the
  giant expands with increasing angular momentum
  (hep-th/0003075)

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What is a giant graviton?

• The dual field theory operators for giants are
  quite well understood
• Using a spin chain one can examine the dynamics
  of an open string with boundary conditions
  specified by the giant graviton (hep-th/0502172)

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Our work

• Found giant graviton solutions in the deformed
  background for some of the BPS states
• Calculated the spectrum of fluctuations for these
  objects in the AdS part of the space and
  recovered known results in the appropriate limit

9
Our work

• Generalised the spin chain approach for
  calculating open string dynamics to accommodate
  the deformations
• From this computed a semi-classical Hamiltonian
  for the open strings
• Calculated a semi-classical Hamiltonian from the
  string worldsheet sigma model

10
Results

• The giants have a higher energy than the
  pointlike graviton, implying that they are
  unstable. Thus one can argue that the agreement
  in this background is a product of the dynamics,
  rather than a relic of symmetries protecting the
  objects.
• The Hamiltonian from the deformed gauge theory
  exactly reproduces the gravity deformations.

11
Future possibilities

• There have been signs that in another deformation
  of the S5 there may be cases when the massive
  giant has a lower energy than the point giant and
  is thus stable. This would imply that gravitons
  can acquire a mass.
• Although SUSY was broken, the field theory still
  possessed a conformal invariance, which is not a
  feature of QCD.

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Future possibilities

• The spectrum for open strings attached to the
  giants should be calculated in the field theory
  and gravity descriptions, and compared.