String scattering amplitudes and mutual information in confining backgrounds: The partonic behavior

Using AdS/CFT methods in various holographic confining backgrounds, we present the connections between the behaviors of string scattering amplitudes and mutual information. We specifically lay down the analogies between the logarithmic branch cut behavior of the string scattering amplitude in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>4</a:mn><a:mi>d</a:mi></a:math>, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi mathvariant="script">A</c:mi><c:mn>4</c:mn></c:msub></c:math>, at low and medium Mandelstam variable <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>s</f:mi></f:math>, which is due to the dependence of the string tension on the holographic radial coordinate, and the branch cut behavior observed in mutual information and critical distance <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>D</h:mi><h:mi>c</h:mi></h:msub></h:math> at low cut-off variable <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>u</j:mi><j:mrow><j:mi>K</j:mi><j:mi>K</j:mi></j:mrow></j:msub></j:math>. In both cases, as <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>s</l:mi></l:math> or <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>u</n:mi><n:mrow><n:mi>K</n:mi><n:mi>K</n:mi></n:mrow></n:msub></n:math> increases, the peaks of the branch cuts fade away in the form of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>Re</p:mi><p:mo stretchy="false">[</p:mo><p:msub><p:mi mathvariant="script">A</p:mi><p:mn>4</p:mn></p:msub><p:mo stretchy="false">]</p:mo><p:mo>∝</p:mo><p:msup><p:mi>s</p:mi><p:mrow><p:mo>−</p:mo><p:mn>1</p:mn></p:mrow></p:msup></p:math>. Next, the modular flow and modular Hamiltonian as the intermediate quantities will be used to further shed light on this connection. We then explain how mutual information itself can act as a probe of chaos in various scenarios. For two examples of Compton scattering (of a photon entangled with another photon off a target) and also the decay of a highly excited string into two tachyons, the pattern of entanglement entropy and the change in the mutual information will be examined. Finally, the kink-kink and kink-antikink scatterings, as simple models of scattering in confining geometries, are employed to probe the fractal structures in the scatterings of topological defects.