Abstract:We study open string amplitudes with the D3-branes in type IIB superstring theory compactified on C 2 /Z 2 . We introduce constant graviphoton background along the branes and calculate disk amplitudes using the NSR formalism. We take the zero slope limit and investigate the effective Lagrangian on the D3-branes deformed by the graviphoton background. We find that the deformed Lagrangian agrees with that of N = 2 supersymmetric U (N ) gauge theory defined in non(anti)commutative N = 1 superspace by choosing app… Show more
“…Here I, J = 1, 2 are SU(2) R R-symmetry indices. It has been shown in [21] that symmetricsymmetric (S,S) type field strength F (αβ)(IJ) corresponds to the non-singlet deformation. An antisymmetric-antisymmetric (A,A) type field strength F [αβ] [IJ] is expected to correspond to the singlet deformation [17].…”
We study the ADHM construction of instantons in N = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(−1) branes at the orbifold singularity of C 2 /Z 2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(−1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the Ω-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.
“…Here I, J = 1, 2 are SU(2) R R-symmetry indices. It has been shown in [21] that symmetricsymmetric (S,S) type field strength F (αβ)(IJ) corresponds to the non-singlet deformation. An antisymmetric-antisymmetric (A,A) type field strength F [αβ] [IJ] is expected to correspond to the singlet deformation [17].…”
We study the ADHM construction of instantons in N = 2 supersymmetric Yang-Mills theory deformed in constant Ramond-Ramond (R-R) 3-form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(−1) branes at the orbifold singularity of C 2 /Z 2 in the same R-R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(−1)-branes to the R-R background. We improve the deformed action by adding a term with space-time dependent gauge coupling. Although the space-time action differs from the action in the Ω-background, both actions lead to the same instanton equations of motion at the lowest order in gauge coupling.
“…In [18,19] we discussed the deformation of N = 2 and N = 4 super Yang-Mills theories in the R-R background field strength of the form F αβAB , where α and β label the spinor indices of (Euclidean) space-time and A and B are internal spinor indices. We classify the field strength into four types F (αβ)(AB) , F [αβ](AB) , F (αβ) [AB] and F [αβ] [AB] .…”
We study deformation of N = 2 and N = 4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In N = 4 case we find that all supersymmetries are broken for generic deformation parameter but part of supersymmetries are unbroken for special case. We also find that classical vacua admit fuzzy sphere configuration. In N = 2 case we determine the deformed supersymmetries. We rewrite the deformed Lagrangians in terms of N = 1 superspace, where the deformation is interpreted as that of coupling constants.
“…Such deformations are realised on the worldvolume of D-branes in RR backgrounds [22,23,24,25,26], and the gravity dual of such a field theory has been constructed in [27]. Also, a graviphoton background gives rise to a noncommutativity between spacetime and superspace coordinates [23,28,29,30,31]. Noncommutative deformations generated by the N S − N S and graviphoton backgrounds do not break any supersymmetry.…”
In this paper we consider non-anticommutative field theories in N = 2 superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry even in the presence of a boundary. We also analyse the partial breaking of supersymmetry caused by non-anticommutativity between fermionic coordinates. Unlike in four dimensions, in three dimensions a theory with N = 1/2 supersymmetry cannot be obtained by a non-anticommutative deformation of an N = 1 theory. However, in this paper we construct a three dimensional theory with N = 1/2 supersymmetry by studying a combination of non-anticommutativity and boundary effects, starting from N = 2 supersymmetry.
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