Abstract
We study the correspondence between ${\mathrm{AdS}}_{3}$ massive IIA supergravity vacua and two-dimensional $\mathcal{N}=(0,4)$ quiver quantum field theories. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space that provide the dual quiver theory with exactly the correct amount of flavor symmetry in order to cancel its gauge anomalies. Then we propose that the structure of the field theory should be complemented with additional bifundamental matter, which we argue may only be $\mathcal{N}=(4,4)$ hypermultiplets. Finally, we construct a Bogomol'nyi-Prasad-Sommerfield (BPS) string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator. During this holographic synthesis, we uncover some interesting features of the quiver superpotential and associate the proposed operator with the same classical mass of its dual BPS string.
Highlights
The AdS=CFT correspondence constitutes a primo realization of the holographic principle while it ties string theory to the most well-studied particle theories we possess
The dual physics of these vacua is generally described by supersymmetric conformal field theories (SCFTs), which for d < 4 are assumed to be strongly coupled IR fixed points
Each SUðNÞ gauge theory living on N D2 or D6 color branes is represented by a gauge node that yields a N 1⁄4 ð4; 4Þ vector multiplet
Summary
The AdS=CFT correspondence constitutes a primo realization of the holographic principle while it ties string theory to the most well-studied particle theories we possess. While over the years many type II supergravity solutions have made their appearance in the holographic arena, there is a certain kind that has recently been popping up more frequently and has become quite popular These are supergravity backgrounds whose entirety of fields is defined by functions of the coordinates of the internal manifolds and are dual to supersymmetric quiver gauge theories. Such multiplets bind color D2-branes with flavor D4-branes and color D6-branes with flavor D8branes, while it is shown that those may only be N 1⁄4 ð4; 4Þ hypermultiplets corresponding to suspended superstrings between D2- and D4-branes or D6- and D8-branes in the ancestral Hanany-Witten setup The existence of this new matter complements the quiver structure, while it seems to be vital in the construction of the dual operator for a particular Bogomol’nyi-PrasadSommerfield (BPS) string state. V we construct a BPS string soliton and propose a dual operator, which both seem to exhibit the same classical mass
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