On Interactions in Higher Spin Gauge Field Theory. Karapet Mkrtchyan. Supersymmetries and Quantum Symmetries July 18-23, 2011 Dubna. Based on work in collaboration with Ruben Manvelyan and Werner Rühl. Based On.
On Interactions in Higher Spin Gauge Field Theory
Supersymmetries and Quantum Symmetries July 18-23, 2011 Dubna
Based on work in collaboration with Ruben Manvelyan and Werner Rühl
Equation of motion for Higher Spin gauge fields
Free Lagrangian for Higher Spin gauge fields
The most elegant and convenient way of handling symmetric tensors is by contracting them with the s’th tensorial power of a vector
Fronsdal fields , Equation and Lagrangian
de Donder operator
de Donder gauge
Power Expansion of Lagrangian
and Gauge transformation
First nontrivial interaction – cubic Lagrangian
Noether equation in first nontrivial order
The Noether equation in this order is equivalent to
Unique Cubic Interaction for arbitrary HS fields!!!
“Symmetry dictates the form of interaction.”C. N. Yang
Cubic Interaction Lagrangian leading term
With the number of derivatives
Generating Function for totally symmetric HS fields
With following gauge transformations
Generating function for gauge parameters
Generating Function for HS cubic interactions
Sagnotti-Taronna GF (On-Shell)
With vertex operator
This result is derived from String Theory side and in complete agreement with results presented here, derived by pure field theory approach!
Off-shelling the On-shell expressions
Off-Shell Generating Function
Simple example: cubic selfinteraction of the graviton in deDonder gauge
Minimal selfinteractions for higher spin gauge fields is a closed subset of all interactions in flat space.
Thank you for your attention