Satchidananda Naik

Academic Report - Physics

Academic Report - Main

Annual Report:2003 - 04

Annual Report - Main

Satchidananda Naik

Research Summary:

The Non-Perturbative N = 2 SUSY Yang-Mills Theory from Semiclassical Absorption of Supergravity by Wrapped D Branes

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 behavior of the N =2 SYM is produced by this duality. The conventional folklore is that the instantons 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). Since the wrapped D5 branes are far from being conformal, the usual holographic description of bulk-boundary connection is quite subtle to extract all the properties of SUSY Yang-Mills theories. This fact led us to wonder about other ways of getting complete picture of the non-perturbative solution of the SUSY Yang-Mills from gravity. It is a fact in quantum field theory that the absorption/emission cross section of particles is always given by the discontinuities of the two point functions of the currents to which the field couples. To be precise, if the interaction Lagrangian is
S_int = &int d⁴x&phi(x)J(x),
then the cross section is, &sigma =

1

2i&omega Disc Π(p) _{p⁰= ω,p^→= 0}
where

Π(p) = &int d⁴x e^ip.x⟨J(x)J(0)⟩.

The trace of the energy-momentum tensor, the γ trace of the super current and the divergence of U(1) axial current due to the R-symmetry form different components of the superconformal anomalous current J_αα^⋅ and its super divergence D^{‾α^⋅}J_αα^⋅ is classically zero however possesses anomaly. More explicitly

⟨√g &theta_μ^μ⟩ =

β(g)

g³

F_μν^a

^{^{^²}}

c(g²)

16π²

W_μνρσ

^{^{^²}}

a(g²)

16π²

R^∼_μνρσ

^{^{^²}}

⟨∂^μ√g &theta_μ^μ⟩ = – 1

2 β(g)

3g³ F_μν^aF^∼aμν ^{^{^²}} + c(g²) - a(g²)

16π² R^∼R

⟨√g γ^μS_μ⟩ = 1

2 β(g)

g³ (σ_μνλ^aF^aμν) + 1

2 R^μνρσσ_ρσ (D_μψ_ν-D_νψ_μ) – (ε^μνρσγ₅ψ_μA_ν^aF_ρσ^a)

where β(g) is the beta function of SYM, a(g) and c(g) are central functions near the criticality, W_μνρσ is the Weyl tensor and R^∼_μνρσ is the dual of the curvature tensor and ψ_μ is the gravitino field. We first derive the world volume action of the wrapped D5 brane where these currents are minimally coupled to the ten dimensional supergravity fields. We show the absorption of dilaton, fluctuating part of RR-2 forms and the gravitino by the world volume of wrapped D5 branes and evaluate the central functions. Consequently we derive the equation relating the pre-potential with the vacuum expectation of the anomaly multiplet.

Publications:

The Non-Perturbative ${\cal N}=2$ SUSY Yang-Mills Theory from Semiclassical Absorption of Supergravity by Wrapped D Branes [JHEP 06 (2004) 022]

Invited Lectures/Seminars:
The Non-Perturbative ${\cal N}=2$ SUSY Yang-Mills from Supergravity, seminar given at Institute of Physics Bhubaneswar

Courses Given:
Advanced Particle Physics at HRI in 1st Semester