Supergravity dual for Ishibashi-Kawai-Kitazawa-Tsuchiya holography

The Ishibashi-Kawai-Kitazawa-Tsuchiya matrix model, from the holographic perspective, arises at the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>p</a:mi> <a:mo>=</a:mo> <a:mo>−</a:mo> <a:mn>1</a:mn> </a:math> end point of the family of dualities relating type II supergravities on near-horizon <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi mathvariant="normal">D</c:mi> <c:mi>p</c:mi> </c:mrow> </c:math> brane geometries to ( <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mrow> <f:mi>p</f:mi> <f:mo>+</f:mo> <f:mn>1</f:mn> </f:mrow> </f:math> )-dimensional super Yang-Mills theories with 16 supercharges. In this work, we detail and expand results reported in a recent paper by establishing the holographic dictionary between gauge-invariant operators in the lowest Bogomol’nyi-Prasad-Sommerfield multiplet of the matrix model and the corresponding Kaluza-Klein fluctuations of Euclidean IIB supergravity compactified on the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mi mathvariant="normal">D</h:mi> <h:mo stretchy="false">(</h:mo> <h:mo>−</h:mo> <h:mn>1</h:mn> <h:mo stretchy="false">)</h:mo> </h:mrow> </h:math> instanton background. The full nonlinear dynamics of these fluctuations can be encoded in a one-dimensional maximal gauged supergravity, which we construct explicitly. We provide its complete Lagrangian, up to second order in fermions, together with the corresponding supersymmetry transformations. We further discuss real forms of the theory for noncompact gauge groups and their embeddings into ten-dimensional supergravities with Lorentzian signature. From the analysis of the one-dimensional Killing spinor equations, we derive different classes of half-supersymmetric solutions, and discuss their uplifts as well as their relations to known solutions.