Satchidananda Naik


Research Summary:

The Gravity dual of the Non-Perturbative $ N = 2 $ SUSY Yang-Mills Theory

Recently the gauge theory/gravity duality , which is commonly known as Ads/CFT duality is extended to non-conformal pure ${\cal N}=1$ or ${\cal N}=2$ supersymmetric Yang -Mills (SYM) theories. So far the perturbative behaviour of the ${\cal N}=2$ SYM is produced by this duality. The conventional folklore is that the instatons which are responsible for the non-perturbative part of the pre-potential are suppressed in the large N limit (since the gauge gravity duality is valid only in the large N limit).

Also the non-perturbative strong coupling behaviour of SYM concerns the dilaton which is plagued with the singularity of "enhancon". Here we establish the anomalous super conformal Ward identity for ${\cal N}=2$ SYM in the gravity dual picture. Further the super conformal Ward identity is written as Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from which one can obtain the exact pre-potential. We start with type IIB little string theory e la' a collection of a large number of $NS_5$ brane in the vanishing string coupling limit which gives rise to $D =6$ SYM . Then we dimensionally reduce two of its spatial world volume in such a way that we retain ${\cal N}=2$ SYM in the low energy limit. The $NS_5$ brane has $SO(4)$ R-symmetry as the normal bundle. When one identifies the $U(1)$ subgroup of the $SO(4)$ R-symmetry with the $U(1)$ spin connection of the two cycle which is compactified, one gets a covariant constant spinor and SUSY is retained, which is commonly known as twisting . This is called wrapping of $NS_5$ brane on a supersymmetric two cycles. If the compact space is a two-shere, then there will be no extra hyper- multiplet and in the low energy limit i.e. in the scale much lower than the radius of the sphere we will get the pure ${\cal N}=2$ SYM. We establish here the anomalous super conformal Ward identity for pure ${\cal N}=2$ SYM.


Publications:

  1. The Sigma model formulation of type II string theory in the $Ads_5\times S_5$ backgrounds with Ramond-Ramond flux , IJMP A, 18 (2003) 1749
  2. The Gravity dual of the Non-Perturbative $ N = 2 $ SUSY Yang-Mills Theory , Proceedings of PASCOS,2003


Preprints:

  1. The Gravity dual of the Non-Perturbative $ N = 2 $ SUSY Yang-Mills Theory, hep-th-0304202


Conference/Workshops Attended:

IXth International Symposium on Particles, Strings and Cosmology TIFR, Mumbai, India, January 3-8, 2003

Visits to other Institutes:

  1. The Abdus Salam ICTP, Trieste, Italy
  2. The Niels Bohr Institute, Copenhagen, Denmark
  3. Tata Institute of Fundamental Research, Mumbai

Invited Lectures/Seminars:

  1. The Non-Perturbative $ N = 2 $ SUSY Yang-Mills from Supergravity, seminar given at The Niels Bohr Institute, Copenhagen, Denmark.
  2. The Gravity dual of the Non-Perturbative $ N = 2 $ SUSY Yang-Mills Theory, Lecture given at PASCOS'03, TIFR, Mumbai.

 



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