Inequivalent light-cone gauge-fixings of strings on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mi>n</mml:mi></mml:msup></mml:math> backgrounds

Abstract

Light-cone gauge-fixed sigma models on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>AdS</a:mi><a:mi>n</a:mi></a:msub><a:mo>×</a:mo><a:msup><a:mi>S</a:mi><a:mi>n</a:mi></a:msup></a:math> backgrounds play an important role in the integrability formulation of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>AdS</c:mi><c:mo>/</c:mo><c:mi>CFT</c:mi></c:mrow></c:math> correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>T</e:mi><e:mover accent="true"><e:mi>T</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mover accent="true"><i:mi>J</i:mi><i:mo stretchy="false">˜</i:mo></i:mover><i:msub><i:mi>T</i:mi><i:mi>τ</i:mi></i:msub></i:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>J</m:mi><m:msub><m:mi>T</m:mi><m:mi>σ</m:mi></m:msub></m:math>, and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mi>J</o:mi><o:mi>τ</o:mi></o:msup></o:math> deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>AdS</q:mi><q:mn>5</q:mn></q:msub><q:mo>×</q:mo><q:msup><q:mi>S</q:mi><q:mn>5</q:mn></q:msup></q:math>, compute the different light-cone gauge symmetry algebras, well known to be <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi mathvariant="fraktur">psu</s:mi><s:mo stretchy="false">(</s:mo><s:mn>2</s:mn><s:mo stretchy="false">|</s:mo><s:mn>2</s:mn><s:msup><s:mrow><s:mo stretchy="false">)</s:mo></s:mrow><s:mrow><s:mo stretchy="false">⊕</s:mo><s:mn>2</s:mn></s:mrow></s:msup><s:mo stretchy="false">⊕</s:mo><s:mi mathvariant="fraktur">u</s:mi><s:mo stretchy="false">(</s:mo><s:mn>1</s:mn><s:msup><s:mrow><s:mo stretchy="false">)</s:mo></s:mrow><s:mrow><s:mo stretchy="false">⊕</s:mo><s:mn>2</s:mn></s:mrow></s:msup></s:mrow></s:math> for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models. Published by the American Physical Society 2024

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