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Motivation World-Sheet SUSY Lie superalgebras From World-Sheet SUSY to Supertargets Outlook N = (2, 2) construction • Sugawara Virasoro tensor T (z) = 1 2 (:Ji J i : + :J i J i : + :∂χ i χ i : − :χ i ∂χ i :) • Fermionic currents G + (z) = J i χ i − 1 2 c ij k :χ i χ j χ k : G − (z) = J i χ i − 1 2 f ij k :χ i χ j χ k : • U(1) current U(z) = :χ i χ i : +ρ k J k + ρ k J k + c i mn f mn j :χ j χ i : . where ρ = −[x i , x i ]
Motivation World-Sheet SUSY Lie superalgebras From World-Sheet SUSY to Supertargets Outlook Deformations • Wide range of deformations with background charges • Define a 0 a 0 = {x ∈ g | (x, y) = 0 ∀ y ∈ [a + , a + ] ⊕ [a − , a − ]} • a = p i x i + q i x i ∈ a 0 G a + = G + + q i ∂χ i • Implies G − a = G − + p i ∂χ i U a (z) = U(z) + p i I i (z) − q i I i (z) T a (z) = T (z) + 1 2 (pi ∂I i (z) + q i ∂I i (z)) • Super-version of affine currents I i = J i − c k ij :χ j χ k : − 1 2 f jk i :χ j χ k : I i = J i − f ij k :χ j χ k : − 1 2 c jk i :χ j χ k :
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