Saturation of the Quantum Null Energy Condition in Far-From-Equilibrium Systems

The Quantum Null Energy Condition (QNEC) is a new local energy condition that a general Quantum Field Theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the entanglement entropy in the corresponding null direction. We present the first series of explicit computations of QNEC in a strongly coupled QFT, using holography. We consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For vacuum and the thermal phase QNEC is always weaker than NEC. While for the homogeneous quench QNEC is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction.Comment: 5 pages, 5 figure

Exploring nonlocal observables in shock wave collisions

We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy.Comment: 28 pp, 9 figs; v2: updated references, changed color bars in Figure 2 and Figure

Quantum Null Energy Condition and its (non)saturation in 2d CFTs

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT$_2$). We show that QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by $h/4$ in the large $h$ expansion.Comment: 37 pages, 9 figures; comments are welcom

Evaluation of autoantibodies as predictors of treatment response and immune‐related adverse events during the treatment with immune checkpoint inhibitors: a prospective longitudinal pan‐cancer study

BACKGROUND: The presence of autoantibodies in the serum of cancer patients has been associated with immune‐checkpoint inhibitor (ICI) therapy response and immune‐related adverse events (irAEs). A prospective evaluation of different autoantibodies in different cancer entities is missing. MATERIALS AND METHODS: In this prospective cohort study, we included a pan‐cancer cohort of patients undergoing ICI treatment and measured a comprehensive panel of autoantibodies at treatment start and at the time point of first response evaluation. The presence and induction of autoantibodies (ANA, ENA, myositis, hepatopathy, rheumatoid arthritis) in different cancer entities were assessed and the association between autoantibodies and disease control rate (DCR), objective response rate (ORR), and progression‐free survival (PFS), as well as the development of grade 3 or higher irAEs were evaluated by logistic regression models, cox proportional hazard models, and Kaplan–Meier estimators. RESULTS: Of 44 patients with various cancer entities, neither the presence of any positive autoantibody measurement nor the presence of positive antinuclear antibodies (ANA) [≥1:80] at baseline was associated with the examined clinical endpoints (DCR, ORR, PFS) in univariable and multivariable analyses. After 8–12 weeks of ICI treatment, DCR, ORR, and PFS did not significantly differ between patients with and without any positive autoantibody measurement or positive ANA titers. The frequency of irAEs did not differ depending on autoantibody status of the patients. CONCLUSION: Autoantibodies at treatment initiation or induction after 8–12 weeks of ICI treatment are not associated with treatment efficacy as indicated by DCR, ORR, and PFS or higher grade irAEs

Patterns of peripheral blood B-cell subtypes are associated with treatment response in patients treated with immune checkpoint inhibitors: a prospective longitudinal pan-cancer study

BACKGROUND: Immune checkpoint inhibitors (ICIs) have revolutionized systemic anti-tumor treatments across different types of cancer. Nevertheless, predictive biomarkers regarding treatment response are not routinely established yet. Apart from T-lymphocytes, the humoral immunity of B-lymphocytes is studied to a substantially lesser extent in the respective setting. Thus, the aim of this study was to evaluate peripheral blood B-cell subtypes as potential predictors of ICI treatment response. METHODS: Thirty-nine cancer patients receiving ICI therapy were included into this prospective single-center cohort study. All had a first blood draw at the date before treatment initiation and a second at the time of first response evaluation (after 8-12 weeks). Seven different B-cell subtypes were quantified by fluorescence-activated cell sorting (FACS). Disease control- (DCR) and objective response rate (ORR) were co-primary study endpoints. RESULTS: Overall, DCR was 48.7% and ORR was 25.6%, respectively. At baseline, there was no significant association of any B-cell subtype with neither DCR nor ORR. At the first response evaluation, an increase in the frequency of CD21(-) B-cells was a statistically significant negative predictor of response, both regarding DCR (OR=0.05, 95%CI=0.00-0.67, p=0.024) and ORR (OR=0.09, 95%CI=0.01-0.96, p=0.046). An increase of the frequency of switched memory B-cells was significantly associated with reduced odds for DCR (OR=0.06, 95%CI=0.01-0.70, p=0.025). Patients with an increased frequency of naïve B-cells were more likely to benefit from ICI therapy as indicated by an improved DCR (OR=12.31, 95%CI=1.13-134.22, p=0.039). CONCLUSION: In this study, certain B-cell subpopulations were associated with ICI treatment response in various human cancer types

Numerical relativity, holography and the quantum null energy condition

Die Quanten-Null-Energiebedingung (QNEC) ist die einzige bekannte, lokale Energiebedingung für Quantentheorien. Im Gegensatz zu den klassischen Energiebedingungen wurde QNEC nicht postuliert, sondern hat ihren Ursprung in der Quanten-Fokussierungs-Vermutung. Außerdem wurde sie bereits für mehrere Spezialfälle und allgemein in mehr als drei Raumzeitdimensionen bewiesen. Des Weiteren ist ihr zentraler Bestandteil eine intrinsisch quantenmechanische Observable, die Verschränkungsentropie. Die direkte Berechnung der Verschränkungsentropie in einer Quantenfeldtheorie ist extrem schwierig, während sie unter Verwendung des holographischen Prinzips durch eine einfache geometrische Größe bestimmt werden kann. Das holographische Prinzip stellt eine Beziehung zwischen Eichtheorien ohne Gravitation und Quantengravitationstheorien mit einer zusätzlichen Dimension her. Das bekannteste Beispiel für diese Dualität ist die AdS/CFT Korrespondenz. Holographie bietet die Möglichkeit sowohl etwas über stark gekoppelte Feldtheorien als auch über Quantengravitation zu lernen. Das Studium von QNEC wird in diesem Zusammenhang zweifellos zu neuen Erkenntnissen führen. Der Fokus dieser Arbeit liegt auf 2- und 4-dimensionalen Feldtheorien. Wir untersuchen unterschiedlich komplexe Systeme mit numerischen und (sofern möglich) analytischen Methoden. Im Vakuum, in thermischen Zuständen, Ungleichgewichtszust ̈anden und einem Modell für Schwerionen-Kollisionen ist QNEC immer erfüllt und manchmal auch gesättigt. Gleichzeitig kann QNEC stärker oder schwächer als die klassische Null-Energiebedingung sein. Interessant ist, dass QNEC in zwei Dimensionen bei Vorhandensein von Materie in der Gravitationstheorie nicht gesättigt sein kann. Die Rückwirkung eines massiven, skalaren Teilchens auf die Geometrie bietet ein gutes Beispiel, bei dem sogar die Differenz zur Sättigung bekannt ist. Betrachtet man hingegen ein massives, selbst-wechselwirkendes Skalarfeld, führt das Potential zu Phasen ̈uberg ̈angen von kleinen zu großen schwarzen Löchern. Wir verwenden QNEC in der dualen Feldtheorie als Werkzeug, um stark gekoppelte, dynamische Systeme besser zu verstehen. Aus den Eigenschaften von QNEC im Grundzustand kann man bereits Aussagen über Phasenübergänge in den thermischen Zuständen treffen.The quantum null energy condition (QNEC) is the only known consistent localenergy condition in quantum theories. Contrary to the classical energy condition which are simply postulated and known to be violated in some classical systems and quantum field theory, QNEC is a consequence of the more general quantum focussing conjecture. It has been proven for several special cases and in general for quantum field theories in three or more spacetime dimensions. QNEC involves an intrinsically quantum property of the theory under consideration, the entanglement entropy. While entanglement entropy is notoriously hard to calculate in quantum field theory, the holographic principle provides a simple geometric description. In general the holographic principle relates a gauge theory without gravity to a theory of quantum gravity in one dimension higher. The most famous example of this gauge/gravity duality is the AdS/CFT correspondence. Holography provides a way to learn about strongly coupled field theories as well as quantum gravity and investigating QNEC in this context will undoubtedly lead to new insights. In this thesis the focus is put on 2- and 4-dimensional field theories, where we study systems of increasing complexity with numerical and (whenever possible) analytical methods. In vacuum, thermal states, globally quenched states and a toy model for heavy ion collisions we find that QNEC is always satisfied and sometimes saturated, while it can be a stronger or weaker condition than the classical null energy condition. Interestingly in two dimensions QNEC cannot be saturated in the presence of bulk matter. The backreaction of a massive scalar particle provides an example where the finite gap to saturation is precisely known. Considering a massive self-interacting scalar field coupled to Einstein gravity leads to phase transitions from small to large black holes, determined by its potential. The dual field theory provides a rich example to use QNEC as a tool to learn about strongly coupled dynamical systems. In particular knowing QNEC in the ground state allows us to make statements about the phase structure of the thermal states.11

Holographic entanglement entropy in heavy ion collisions

Zusammenfassung in deutscher SpracheUnter Verwendung holographischer Methoden rechnen wir die Zweipunkt- Korrelationsfunktion und die Entanglement Entropie für Schwerionen-Kollisionen aus, welche als Kollision von Gravitationsschockwellen in 5 dimensionaler Anti-de Sitter Raumzeit modelliert werden. Die Berechnung dieser Größen reduziert sich auf der Seite der Gravitationstheorie auf die Berechnung extremaler Flächen (bzw. Geodäten, unter Verwendung der Symmetrie der untersuchten Region). Im Rahmen dieser Arbeit wurde ein Mathematica Package entwickelt, das diese Berechnungen mittels Relaxationsmethoden für verschiedene Szenarios ausführen kann. Unter Verwendung zweier verschiedener Anfangsbedingungen, breiten und schmalen Schockwellen, zeigt sich qualitativ unterschiedliches Verhalten der berechneten Größen. Das erlaubt es, die Entanglement Entropie als Ordnungsparameter für die Unterscheidung zwischen Transparenz und vollem Abstoppen der kollidierenden Schockwellen zu verwenden.Using the methods of holography we calculate the two-point function and entanglement entropy in heavy ion collisions, modeled by colliding gravitational shock waves in Anti-de Sitter spacetime. The calculation reduces to finding extremal surfaces (or geodesics, using the symmetry of the investigated boundary region) in the gravitational problem. A Mathematica package, capable of finding geodesics for several different scenarios using relaxation methods, was developed as part of this work. Using two different initial conditions, wide and narrow shock waves, we find qualitatively different behavior of the calculated quantities. This allows to use the entanglement entropy as order parameter to distinguish between the transparency and full stopping scenario of colliding shock waves.6

Quantum null energy condition and its (non)saturation in 2d CFTs

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT$_2$). We show that QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by $h/4$ in the large $h$ expansion

Quantum Null Energy Condition and its (non)saturation in 2d CFTs

We consider the Quantum Null Energy Condition (QNEC) for holographic conformal field theories in two spacetime dimensions (CFT$_2$). We show that QNEC saturates for all states dual to vacuum solutions of AdS$_3$ Einstein gravity, including systems that are far from thermal equilibrium. If the Ryu-Takayanagi surface encounters bulk matter QNEC does not need to be saturated, whereby we give both analytical and numerical examples. In particular, for CFT$_2$ with a global quench dual to AdS$_3$-Vaidya geometries we find a curious half-saturation of QNEC for large entangling regions. We also address order one corrections from quantum backreactions of a scalar field in AdS$_3$ dual to a primary operator of dimension $h$ in a large central charge expansion and explicitly compute both, the backreacted Ryu--Takayanagi surface part and the bulk entanglement contribution to EE and QNEC. At leading order for small entangling regions the contribution from bulk EE exactly cancels the contribution from the back-reacted Ryu-Takayanagi surface, but at higher orders in the size of the region the contributions are almost equal while QNEC is not saturated. For a half-space entangling region we find that QNEC is gapped by $h/4$ in the large $h$ expansion