Supersymmetric D-brane probes in 4D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="script">N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/

We extend the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>κ</a:mi> </a:math> -symmetry analysis of supersymmetric D-brane probes in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>AdS</c:mi> <c:mn>2</c:mn> </c:msub> <c:mo>×</c:mo> <c:msup> <c:mi mathvariant="bold">S</c:mi> <c:mn>2</c:mn> </c:msup> </c:math> attractor geometry, originally performed by Simons, Strominger, Thompson, and Yin to also include stationary—but nonstatic—worldlines carrying angular momentum along the 2-sphere. We demonstrate that certain special trajectories, with fixed radius and orbital velocity, solve the equations of motion and moreover satisfy a supersymmetry preserving condition, thus defining new <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mfrac> <f:mn>1</f:mn> <f:mn>2</f:mn> </f:mfrac> </f:math> -BPS configurations. Furthermore, these classical paths are shown to saturate a lower bound for the Hamiltonian generating global time translations, with the corresponding minimal energy depending on a generalized angular momentum vector <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mi mathvariant="bold-italic">J</h:mi> </h:mrow> </h:math> . The direction of the latter, in turn, determines exactly which supercharges remain unbroken. Our results reveal a richer spectrum of (multiparticle) supersymmetric states in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:msub> <k:mrow> <k:mi>AdS</k:mi> </k:mrow> <k:mrow> <k:mn>2</k:mn> </k:mrow> </k:msub> <k:mo>×</k:mo> <k:msup> <k:mrow> <k:mi mathvariant="bold">S</k:mi> </k:mrow> <k:mrow> <k:mn>2</k:mn> </k:mrow> </k:msup> </k:mrow> </k:math> , which can be organized into distinct selection sectors labeled by the conserved <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>S</n:mi> <n:mi>U</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>2</n:mn> <n:mo stretchy="false">)</n:mo> </n:math> charges. This construction has direct applications in black hole microstate counting, the analysis of probe dynamics, and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msub> <r:mi>AdS</r:mi> <r:mn>2</r:mn> </r:msub> <r:mo>/</r:mo> <r:msub> <r:mi>CFT</r:mi> <r:mn>1</r:mn> </r:msub> </r:math> holography.