A hundred years ago, Austrian physicist Erwin Schrödinger introduced the equation that now bears his name, a cornerstone of quantum mechanics. Schrödinger’s Equation provides a mathematical framework to calculate the wave function of a system and track how it evolves over time.
Schrödinger’s cat is a thought experiment showing the strangeness of quantum mechanics. Imagine a cat in a sealed box with a device that has a 50% chance to release poison, triggered by a quantum event. Until you open the box, quantum rules say the cat is both alive and dead at the same time—a “superposition.” Only when observed does the cat’s state become definite. It illustrates how observation affects quantum systems. Thus the equation remains central to understanding the behavior of particles at the quantum level.
“Quantum mechanics, along with Albert Einstein’s theory of general relativity, are the two pillars of modern physics,” says Utah State University (USU) physicist Abhay Katyal. “The challenge is, for more than half a century, scientists have struggled to reconcile these two theories.”
Katyal, a doctoral student and Howard L. Blood Graduate Fellow in the Department of Physics, explains that quantum mechanics governs matter and forces at the subatomic scale, while general relativity describes gravity and the structure of space-time on cosmic scales. The difficulty lies in uniting these frameworks into a single, consistent theory.
“Many unknowns in physics are explained by one side or the other, but these explanations are often incompatible,” says Oscar Varela, associate professor at Utah State University and Katyal’s faculty mentor. “Quantum gravity is an attempt to combine these theories but, to this day, we don’t know what quantum gravity is.”
In their latest work, Varela, Katyal, and former USU postdoctoral fellow Ritabrata Bhattacharya present a new gauging of maximal supergravity in five spacetime dimensions. This gauging involves a gauge group containing ISO(5) and incorporates the local scaling symmetry of the metric, while also admitting a supersymmetric anti–de Sitter vacuum. The researchers show that this maximal supergravity emerges through a consistent truncation of M theory on a six-dimensional geometry linked to a stack of N M5 branes wrapped on a smooth Riemann surface.
The existence of this truncation enables the team to holographically determine the complete, universal spectrum of light operators in the dual four-dimensional 𝒩 = 2 theory of class 𝒮. They further compute the superconformal index of the dual field theory at large N, finding exact agreement with previously established field theory results in specific limits.
Their findings, published in the May 6 online issue of Physical Review Letters and supported by the National Science Foundation’s Elementary Particle Physics-Theory program, highlight the "holographic principle" as a central tool in advancing the search for quantum gravity.
“Proposed theories of quantum gravity are difficult to test experimentally because we don’t have the technology to predict effects occurring at extremely high energies or extremely small scales,” Varela says. “For theoretical physicists like us, a precise mathematical model is akin to the apparatus of an experimental physicist: It can be used to make predictions about the physical world.”
For the Utah State team, the holographic principle provides a framework to move closer to a unified description of nature’s laws.
Source: Utah State University, American Physical Society
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