Tensionless Null Strings Advance String Theory Understanding of the ILST Action

Scientists are increasingly investigating the behaviour of strings at extreme energies, moving beyond the established link between string theory and Einsteinian gravity to explore the tensionless limit. Arjun Bagchi from the Indian Institute of Technology Kanpur, Aritra Banerjee from Birla Institute of Technology and Science, Pilani Campus, and Ritankar Chatterjee from the Beijing Institute of Mathematical Sciences and Applications, along with Priyadarshini Pandit et al, present a comprehensive review of tensionless null string theory, tracing its origins from the work of Schild to recent advances in understanding its underlying symmetries. This research is significant because it reveals a surprising connection between these strings and Carrollian conformal algebra, suggesting a novel worldsheet description and potentially offering new insights into the fundamental nature of spacetime and gravity, particularly in scenarios involving black holes and compactification.

This research is significant because it reveals a surprising connection between these strings and Carrollian conformal algebra, suggesting a novel worldsheet description and potentially offering new insights into the fundamental nature of spacetime and gravity, particularly in scenarios involving black holes and compactification.

Tensionless Strings and Carrollian Worldsheet Symmetries

Tensionless strings, also known as null strings, sweep out null worldsheets in target space, presenting a unique approach to understanding fundamental physics. Recent research centres on the emergence of the Carrollian Conformal Algebra as residual worldsheet symmetries within the ILST action, identifying the tensionless limit as a worldsheet Carrollian limit on the string worldsheet. Symmetries, constraints, and mode expansions, computed from both perspectives, exhibit a remarkable consistency, serving as a robust cross-check of the analytical methods. This study delves into both closed and open null strings, alongside their supersymmetric counterparts, expanding the scope of investigation into diverse string configurations.

Researchers detail the canonical quantisation and the spectrum of these three theories, meticulously outlining their properties and characteristics. The work further discusses the novel features of these quantum null theories and the impact of compactification on their behaviour, revealing how spatial dimensions influence their dynamics. Furthermore, the study explores Carroll strings and their applications to strings approaching black holes, extending the theoretical framework to extreme gravitational environments. A concise overview of other related developments is also provided, highlighting the broader context of this research within the field of theoretical physics.

The analysis of closed and open strings, alongside their supersymmetric extensions, provides a comprehensive picture of the possible configurations and their associated quantum properties. The discovery of three consistent quantum theories arising from the ILST action represents a significant breakthrough, demanding further investigation into their physical implications and potential connections to observable phenomena. This work opens possibilities for exploring the behaviour of strings in extreme gravitational fields, such as those near black holes, and for developing new approaches to quantum gravity.

Null strings and Carrollian worldsheet symmetries

To achieve this, the team employed canonical quantisation techniques to determine the spectrum of these three theories, meticulously detailing their novel properties and the effects of compactification upon them. This method achieves a precise correspondence between the two frameworks, bolstering confidence in the theoretical underpinnings. The research team developed a framework for analysing the spectrum of states arising in these tensionless theories, calculating central charges for each of the three quantum theories identified. The approach enables a deeper understanding of the fundamental relationship between string theory, gravity, and the intriguing realm of Carrollian physics, potentially offering new avenues for unifying quantum mechanics and classical gravity, a long-standing challenge in theoretical physics. This work builds upon the established Polyakov action for bosonic strings, given by SP = −T 2 ∫ d2ξ√−γγαβ∂αXμ∂βXνημν, where ξα represents worldsheet coordinates and Xμ denotes spacetime coordinates.

Tensionless Null Strings and Carrollian Worldsheet Symmetry

Data shows that these null theories exhibit novel characteristics, and the study details the effect of compactification on their behaviour, opening avenues for further investigation into their properties. Researchers detailed the massless point particle action as S = −m ∫ τA τB dτ p − X2, where X = dX/dτ, and demonstrated that a naive massless limit cannot be obtained directly. The work presents the Stueckelberg action, S = −1/2 ∫ dτ X2, which allows for timelike, spacelike, and null geodesics, addressing the limitations of the original action. Tests prove that the Nambu-Goto action, defined as SNG = T ∫ d2σ p −det γαβ, with γαβ representing the induced worldsheet metric, fails to describe strings tracing null worldsheets due to the requirement of non-zero worldsheet area.

The Schild action, proposed as a string analogue to the Stueckelberg action, is defined as S = 1/4 ∫ d2σ ΓμνΓμν, where Γμν = XμX′ν −X′μ Xν and X′ = ∂σX. Measurements confirm that the equation of motion derived from this action, ∂αΓ2 = 0, allows for Γ2 = 0, thus accommodating null strings as valid solutions. The research highlights that while the Schild action permits null strings, it lacks reparametrization invariance, a challenge addressed by subsequent developments in the field.

Null String Theory Reveals Three Consistent Models

This work examines strings at zero tension, a limit distinct from the conventional point-particle limit which yields Einstein gravity, and explores the emergence of Carrollian conformal algebra as residual worldsheet symmetries. The analysis demonstrates consistency between the classical theory and calculations derived from the Isberg et al action, confirming the robustness of the approach through matching symmetries, constraints and mode expansions. The authors detail the effects of compactification on these novel theories and explore connections to Carroll strings and strings near black holes, including applications to BTZ black holes. Related developments, such as null branes, duality webs, path integral formulations and links to ambitwistor strings and celestial conformal field theory, are also briefly discussed.

The authors acknowledge limitations in the current understanding of the full quantum theory and the challenges associated with consistently incorporating interactions. Future research directions include further exploration of the relationship between null strings and 3D black-hole microstates, as well as a deeper investigation into the potential for a fully consistent quantum theory incorporating these findings. These results offer a valuable contribution to the ongoing effort to reconcile gravity with quantum mechanics, providing new insights into the high-energy regime of string theory and the nature of spacetime itself.