$\beta$-deformations, potentials and KK modes

Abstract

We have studied volumes of the 3-cycle and the compact 5-volumes for the $\beta$ transformed geometry and it comes out to be decreasing except one choice for which the torus do not stay inside the 3-cycle and ``5-cycle.'' There are 3 possible ways to construct these cycles. one is as mentioned above and the other two are, when the torus stay inside the cycle and when both the torus and the cycle shares a common direction. Also, we have argued that under $\beta$ deformation there arises a non-trivial ``potential'' as the $SL(3,R)$ transformation mixes up the fields. If we start with a flat space after the $SL(3,R)$ transformation the Ricci-scalar of the transformed geometry do not vanishes but the transformed solution is reminiscent of NS5-brane. We have explicitly, checked that $\beta$-transformation indeed is a marginal deformation in the gravity side.

18 pp, latex, typos fixed, a minor change, few more typos and a reference fixed

References in corpus (6)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Lax Pair for Strings in Lunin-Maldacena Background
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Marginal Deformations with U(1)^3 Global Symmetry
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• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
• Complex marginal deformations of D3-brane geometries, their Penrose limits and giant gravitons
• Probing Universality in the Gravity Duals of N=1 SYM by gamma-deformations
• Null Melvin Twist to Sakai-Sugimoto model
• Pure Spinor Strings in TsT Deformed Background
• Semiclassical Strings in Electric and Magnetic Fields Deformed $Ad{S}_5\times S^5$ Spacetimes
• Chiral symmetry breaking and restoration from holography
• gamma_i Deformed Lax Pair for Rotating Strings in the Fast Motion Limit
• Deformations of flows from type IIB supergravity
• KK-Masses in Dipole Deformed Field Theories
• $T^3$ deformations and $\beta$-deformed geometries