Symmetries and Strings in Field Theory and Gravity (1011.5120v2)

Abstract: We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an emergent $\Z_p$ one-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear $\sigma$-models. It also allows us to expand on Polchinski's classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.

• The paper proposes that global symmetries vanish in quantum gravity, imposing strict constraints on gauge symmetries including discrete groups and brane charges.
• It demonstrates that all continuous gauge groups are compact, supported by detailed analyses of Kalb-Ramond symmetries and cosmic string classifications.
• The work introduces the completeness hypothesis, asserting that every allowed electric and magnetic charge appears within a consistent quantum field and gravity framework.

Analyzing Symmetries and Strings in Field Theory and Gravity

This paper, written by Tom Banks and Nathan Seiberg, provides a comprehensive examination of symmetries in quantum field theory and quantum gravity, with a particular focus on discrete gauge symmetries. The authors explore the implications of such symmetries on cosmic strings, quantum gravity, and supergravity theories, presenting a unified perspective on several conjectures traditionally understood in the context of quantum gravity.

Key Conjectures in Quantum Gravity

The research highlights three conjectures which form the backbone of the paper’s arguments:

1. Absence of Global Symmetries: The authors claim that global symmetries do not exist in models of quantum gravity, extending this notion to discrete symmetry groups and higher brane charges. This proposition aligns with the understanding that stable branes are associated strictly with gauge symmetries.
2. Compactness of Continuous Gauge Groups: All continuous gauge symmetries, including Kalb-Ramond symmetries, are proposed to be compact. This conjecture precludes the possibility of non-compact gauge groups (like $\mathbb{R}$) existing in these frameworks.
3. Completeness Hypothesis: The full spectrum of allowed electric and magnetic charges, consistent with Dirac quantization, should be present in the theory. This conjecture asserts that any charge allowed by the theory is found within its spectrum, an assertion supported by known examples in string theory contexts.

Implications and Theoretical Discussions

The paper also elaborates on the classification of strings in models of quantum gravity. Specifically, cosmic strings are intrinsically linked to one-form (Kalb-Ramond) gauge symmetries—a major focus across sections of the paper. Interestingly, the document refines existing classifications, such as those by Polchinski, suggesting that stable strings are always coupled to such gauge fields.

The practical implications of these conjectures cascade into numerous aspects of quantum gravity models, voiding potentials for global charges observable at infinity—an attribute attributed to the holographic principle and the Covariant Entropy Bound (CEB). As such, the completeness hypothesis presents a closely intertwined restriction with the nonexistence of global symmetries.

The treatment of discrete symmetries, especially Z$_p$ gauge theories, is articulated through their description via BF-theories—an intricate layering of interactions between one-form and two-form gauge fields. This formulation exposes an emergent gauge symmetry, exemplifying the multifaceted approach the authors employ in expounding upon duality and the interpretation of conventional and novel observables.

Future Trajectory and Theoretical Extensions

Consequential for theoretical physics, these conjectures reshape considerations in constructing unified models and constrain the spectrum of viable theories in quantum gravity. The cross-pollination between gravitational requirements and gauge symmetries raises essential questions about the role these theories play in contemporary physics and astrophysical settings.

Notably, the interaction between supergravity theories and field theoretical models is ventured, as constraints stipulated by string currents and gauge symmetries significantly impact N = 1 supergravity couplings in four dimensions. Central to these extensions are the modifications to FI-terms and the introduction of field-dependent equations that stabilize classical string solutions.

Conclusion

Integrating both classical and current themes in theoretical physics, this paper underscores the complexity and depth of understanding required to address symmetries within quantum frameworks. Through its meticulous dissection of symmetries, strings, and their implications, the paper offers a rich, structured analysis that challenges existing paradigms and paves the way for future explorations within the domain of theoretical physics. Continued studies may seek to address open questions and explore the practical limits of these conjectures, particularly in empirical and cosmological contexts.