Fields Added Break Symmetries, Theory Decompactifies

Scientists are increasingly focused on understanding the boundaries of consistent theoretical physics, particularly concerning non-compact gauge theories and their potential incompatibility with established frameworks. Finn Gagliano and Christopher Tudball, both from Durham University, present research challenging the widely held belief that all such theories reside within the ‘swampland’ , the realm of seemingly consistent theories that ultimately prove physically unrealistic. Their investigation explores whether the troublesome global symmetries accompanying non-compact gauge symmetries can be resolved by invoking an uncountable infinity of fields. The researchers demonstrate that while these symmetries can indeed be broken in this manner, doing so often leads to the breakdown of the effective field theory and, strikingly, can induce decompactification to a higher-dimensional theory, effectively reversing a Kaluza-Klein reduction. This work offers crucial insights into the species scale, free parameters, and the Weak Conjecture, potentially reshaping our understanding of the limits of quantum field theory and the viability of extra-dimensional models. Within the chilled vacuum of theoretical physics, a long-standing puzzle concerning fundamental symmetries has begun to yield. Calculations suggest that constructing consistent theories with certain symmetries necessitates either an infinite number of particles or a shift to a higher-dimensional framework, effectively ‘unwinding’ extra dimensions and placing limits on the kinds of universes that can exist. Scientists are increasingly focused on identifying the boundaries between consistent and inconsistent theories of quantum gravity, a field of study known as the swampland programme. Recent work proposes that effective field theories (EFTs) exhibiting global symmetries are incompatible with a complete theory of quantum gravity, implying these theories reside within the swampland, a space of logically consistent but physically unrealisable models. Researchers have explored whether an uncountable infinity of fields might circumvent restrictions on non-compact gauge theories, offering a potential pathway to avoid the swampland. However, adding an infinite number of fields presents challenges to the validity of the effective field theory. These symmetries can be broken by an infinite spectrum of fields, but the resulting EFT breaks down at a certain scale and may undergo decompactification, a process akin to reversing a Kaluza-Klein reduction. This decompactification leads to a higher-dimensional theory devoid of the original non-compact gauge symmetry. Understanding the implications of infinite field content requires careful consideration of the species scale and the Weak Gravity Conjecture, which posits a relationship between gravity and the strength of gauge interactions. By examining these concepts, scientists are beginning to map out the parameter space where decompactification might occur, potentially revealing a connection between theoretical frameworks. The behaviour of the gauge kinetic term, a component of the theory describing the strength of the gauge interaction, is linked to the Weak Gravity Conjecture and the allowed values of free parameters within the model. At certain points in this parameter space, the infinite volume associated with the non-compact dimension can lead to a vanishing gauge coupling, complicating the picture and suggesting a fundamental limit to the applicability of the EFT. The research delves into the mathematical details of breaking these symmetries, demonstrating how an uncountable infinity of interacting fields can complete the spectrum of operators required for consistency. The analysis reveals a pathway for the R gauge theory, a specific example of a non-compact gauge theory, to decompactify into a higher-dimensional theory without the problematic gauge symmetry, offering a potential resolution to the swampland constraints. Kaluza-Klein reduction and the Weak Gravity Conjecture via gauge kinetic terms A detailed examination of Kaluza-Klein reduction on R was undertaken to establish a foundational understanding of dimensional reduction techniques, analysing how fields transform and how higher-dimensional theories emerge from lower-dimensional ones. This approach provides a concrete mathematical framework for exploring the relationship between gauge symmetries and spacetime geometry. Attention then turned to the gauge kinetic term and its implications for the Weak Gravity Conjecture. Calculations were performed to determine how the gauge kinetic term behaves under the Kaluza-Klein reduction, assessing whether it satisfies the constraints imposed by the Weak Gravity Conjecture, which posits that the coupling constant of a gauge theory must be sufficiently large to allow for the production of black holes. The study extended beyond simple dimensional reduction to consider the implications of an infinite number of fields, investigating whether an infinite number of charged fields could explicitly break global symmetries, completing the spectrum of operators required for consistency. Evaluating such a system necessitated careful consideration of the species scale, a measure of the number of degrees of freedom at a given energy scale. Researchers found that the species scale for the theory with infinitely many fields vanishes in Planck units, indicating that the effective field theory breaks down at all energy scales. However, at restricted points of parameter space, the theory can be decompactified to a higher-dimensional theory with finitely many fields, effectively removing the problematic non-compact gauge symmetry. Supplementary calculations detailed alternative integration methods for evaluating the Noether current and analysed propagators to provide insight into the vanishing species scale, with mass dimensions carefully matched between the original and decompactified theories to ensure consistency. Symmetry breaking and dimensional transition via infinite field introduction The research reveals that introducing an uncountable infinity of fields leads to the breaking of symmetries previously thought to be immutable, specifically causing decompactification, a transition to a higher-dimensional theory. The R gauge theory, when populated with uncountably infinite fields, transforms into a theory lacking the original R gauge symmetry but existing in one additional spacetime dimension. Detailed analysis shows that the addition of these fields alters the behaviour of Wilson lines. For a U(1) gauge theory, introducing even a single charged field disrupts current conservation, immediately breaking the associated symmetry. Introducing an uncountable infinity of fields is required by the R gauge theory to achieve the same effect, as any countable addition leaves a continuum of unscreened Wilson lines. The study carefully examines the species scale, finding it vanishes under certain conditions, linked to the breakdown of the effective field theory. The decompactification process introduces a finite number of parameters into the higher-dimensional theory. The work demonstrates how a theory with an infinite number of fields can effectively reduce to a finite-field theory in a higher dimension, potentially supporting the Weak Conjecture. The decompactification limit matches mass dimensions across the transition, confirming the consistency of the process. Uncountable infinities of fields fail to resolve parameter limitations in quantum gravity Scientists exploring the fundamental laws governing the universe have long grappled with the consistency between quantum mechanics and gravity. Theoretical physicists have sought to reconcile these pillars of modern physics, often encountering mathematical inconsistencies when constructing theories encompassing both. This work addresses the apparent incompatibility of non-compact gauge theories with the requirement that physical theories possess a limited number of definable parameters. Previous attempts to resolve this tension relied on assumptions about the finite nature of physical systems, but this research investigates the possibility that an infinite number of fields might circumvent the restrictions. The findings reveal a surprising outcome: while symmetries can be broken by introducing an uncountable infinity of fields, the effective theory collapses or transforms into a higher-dimensional framework, negating the initial non-compact gauge symmetry. This decompactification resembles a reversal of a Kaluza-Klein reduction, suggesting that the universe may have a preference for certain types of symmetry, and attempts to circumvent these preferences lead to instability. Understanding the implications for the ‘species scale’, a theoretical limit on the number of particle types allowed in a consistent quantum gravity theory, is vital. By examining these infinite field systems, researchers gain insight into the boundaries of viable theoretical models. The reliance on effective field theory introduces a limitation, as it provides only an approximation of reality valid at certain energy scales. This study ventures into the mathematically complex territory of infinite degrees of freedom, demanding careful consideration of convergence and well-definedness. This work represents a shift in perspective, moving beyond the search for finite solutions towards exploring the consequences of infinite possibilities. It highlights the importance of considering not just what is allowed, but also what happens when theoretical boundaries are pushed to their absolute limits. The question of whether nature truly employs such infinite systems remains open, but this research provides a valuable framework for future investigations, potentially guiding the development of more complete and consistent models of the universe. 👉 More information 🗞 Decompactification Limits of Non-Compact Gauge Theory 🧠 ArXiv: https://arxiv.org/abs/2602.15680 Tags: