Type II string theory on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>AdS</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> and symmetric orbifolds

Abstract

We discuss in detail the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:math> -dimensional superconformal field theory dual to type II string theory on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>AdS</c:mi> <c:mn>3</c:mn> </c:msub> <c:mo>×</c:mo> <c:msup> <c:mi>S</c:mi> <c:mn>3</c:mn> </c:msup> <c:mo>×</c:mo> <c:msup> <c:mi>T</c:mi> <c:mn>4</c:mn> </c:msup> </c:math> , emphasizing the string theoretic aspects of this duality. For one unit of Neveu-Schwarz (NS-NS) 5-brane flux ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>Q</e:mi> <e:mn>5</e:mn> </e:msub> <e:mo>=</e:mo> <e:mn>1</e:mn> </e:math> ), this string theory has been suggested to be dual to a grand-canonical ensemble of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mi>T</g:mi> <g:mrow> <g:mn>4</g:mn> <g:mi>N</g:mi> </g:mrow> </g:msup> <g:mo>/</g:mo> <g:msub> <g:mi>S</g:mi> <g:mi>N</g:mi> </g:msub> </g:math> free symmetric orbifold conformal field theories (CFTs). We show how the string genus expansion emerges to all orders for the free orbifold grand-canonical correlation functions. We also discuss how the strong coupling limit of the NS-NS string theory arises (even at large <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>N</i:mi> </i:math> ) in the free orbifold description, and argue why this limit does not have a weakly coupled RR description. The dual conformal field theory (CFT) includes (for all values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>Q</k:mi> <k:mn>5</k:mn> </k:msub> </k:math> ) an extra <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>T</m:mi> <m:mn>4</m:mn> </m:msup> </m:math> factor that is decoupled from perturbative string theory. We discuss the exactly marginal deformations that relate the different values of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>Q</o:mi> <o:mn>5</o:mn> </o:msub> </o:math> , including the precise <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>J</q:mi> <q:mover accent="true"> <q:mi>J</q:mi> <q:mo stretchy="false">¯</q:mo> </q:mover> </q:math> deformations mixing this extra <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>T</u:mi> <u:mn>4</u:mn> </u:msup> </u:math> with the symmetric orbifold. Published by the American Physical Society 2024

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