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Motivation World-Sheet SUSY Lie superalgebras From World-Sheet SUSY to Supertargets Outlook Screening charges in supergroup model • We achieved T + twisted = T GL(N|N) ⇒ S GL(N)×GL(N) N =(1,1) + deformations + twist = S GL(N|N) 0 • Free fermion resolution boson-fermion interaction terms S pert = − 1 4πk • Are screening charges: ∫ Σ d 2 σ str(Ad(g B )(¯b)b) J(z)L pert ∼ total derivatives • Conclusion: Is (classical) SUSY deformation • Is in fact chiral F-term perturbation: Take g B = ( ) A 0 0 B • φ = tr(A −1 B) in (+, +)-ring, has dimension (1/2, 1/2) F ++ = −{G − −1/2 , [Ḡ− −1/2 , φ ++]} = 4π k L pert
Motivation World-Sheet SUSY Lie superalgebras From World-Sheet SUSY to Supertargets Outlook Bosonic screening charges • Free fermion resolution gave us S 0 = Sren WZNW [g B ] − 1 ∫ dz 2√ hR (2) 1 4π 2 ln det R(g B) + 1 ∫ dz 2 ( b a ¯∂c a − 2π ¯b a ∂¯c a) • GL(2) Gauss decomposition exp γ ( ) ( ( ) ( )) 0 1 1 0 1 0 exp φ 0 0 0 + φ 0 1 z exp ¯γ 0 −1 • First order formalism: Introduce auxiliary fields β and ¯β ∫ Sren WZNW [g B ] = S kin+b.g. [φ 0 , φ z , β, γ] + d 2 zβ ¯βe φz/√ k • Screening charges are chiral F-terms. ( ) 0 0 1 0
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