Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory

Abstract: N=2, 4 and 8 supersymmetric string theories in four dimensional flat space-time have moduli space of vacua. We argue that starting from a theory where the moduli approach a particular moduli space point A at infinity, we can construct a classical solution that contains an arbitrarily large space-time region where the moduli take values corresponding to any other moduli space point B of our choice to any desired accuracy. Therefore the observables of a theory with a given set of asymptotic values of the moduli will have complete information on the observables for any other asymptotic values of the moduli. Also it is physically impossible for any experiment, performed over a finite time, to determine the asymptotic values of the moduli. We point out the difference between asymptotically flat space-time and asymptotically AdS space-time in this regard and discuss the possible implication of these results for holographic duals of string theories in flat space-time. For N=2 supersymmetric theories, A and B could correspond to compactifications on topologically distinct Calabi-Yau manifolds related by flop or conifold transitions.

• The paper shows that moduli fields can display distinct interior values from their asymptotic settings, challenging the notion of fixed vacuum expectations.
• The paper employs scaling transformations and nested black hole configurations to systematically generate arbitrary transitions across the moduli space in N=4 and N=8 theories.
• The paper demonstrates that thick domain walls facilitate continuous moduli changes, offering fresh insights into holographic dualities and quantum gravity.

Summary of "Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory"

The paper "Decorating Asymptotically Flat Space-Time with the Moduli Space of String Theory" by Ashoke Sen investigates the intriguing possibility of moduli fields in string theories serving as parameters rather than vacuum expectation values. The exploration centers around N=2, N=4, and N=8 supersymmetric string theories in asymptotically flat four-dimensional space-time, and the ability to construct solutions where moduli fields transition from asymptotic values to other desired values within large interior regions.

Key Results and Methodology

1. Moduli Fields and Asymptotic Values: The paper challenges the conventional belief that moduli fields behave as vacuum expectation values fixed at infinity. Instead, it posits that moduli values in large regions of space-time can differ significantly from their asymptotic values without any detectable boundary signals, rendering it impossible for finite-time experiments to conclusively measure asymptotic moduli values.
2. Scaling Transformations: A crucial tool used throughout the paper is the scaling transformation of solutions, which by dilating coordinates, ensures that local spacetime curvature and field strengths diminish. This flattening allows for vast regions to maintain different moduli values that otherwise match at infinity.
3. Nested Black Hole Solutions: The core methodology employs nested configurations of black holes, which act as localized solutions transitioning between different moduli values. The paper establishes that through proper scaling and nesting, all points in the moduli space can be accessed from any starting point.

• Generation of Arbitrary Moduli Configurations: For N=4 theories, the paper demonstrates using multiple nested black holes with specific charge distributions and transformations to manipulate the moduli matrix M. This enables coverage of the moduli space within finite, nested steps.
• Inclusion of RR Moduli for N=8 Theories: The challenge expands to RR moduli which are not readily accessible via transformations in N=4 theories.

1. Thick Domain Wall Configurations: Aside from black holes, the paper elucidates the use of thick domain walls to generate moduli transitions in areas not readily accessible by black holes alone. These configurations, though less concretely constructed, offer a universal approach to transforming moduli values across arbitrary distances in the moduli space.
2. Implications for AdS Space-Time and Holography: The examination extends to differences between flat and AdS spaces concerning moduli transformation capabilities. In AdS contexts, moduli values appear more rigidly tied to asymptotic boundaries, suggesting distinct physical theories based on boundary parameters, contrasting against the flexibility found in asymptotically flat spaces.

Broader Implications and Future Directions

The analysis introduces profound implications for holography in string theory. By demonstrating that asymptotic moduli values can transition within large spatial domains, it suggests that the identification of asymptotic moduli as vacuum expectations may require reconsideration within holographic dual theories. This revelation could inform future studies in quantum gravity and considerably impact how researchers approach parameterization in holographic models.

This exploration opens pathways to understanding how string theories in flat space could provide content equivalent to having multiple distinct theories, as traditionally perceived in AdS/CFT contexts. Such understanding could lead to groundbreaking methods of encoding dual theories, necessitating innovative conceptual frameworks that transcend traditional limits within current theoretical paradigms.

Conclusion

Ashoke Sen's paper thoroughly critiques the foundational understanding of moduli spaces in string theories, challenging preconceived notions about their behaviors and roles as parameters versus vacuum expectation values. The findings play a critical role in advancing theoretical physics, particularly in gravity theory contexts, regarding how asymptotic and internal space-time characteristics correlate and influence observable phenomena, paving the way for future theoretical and computational advancements in the field.