Periodic Reporting for period 1 - NRST (Foundation of Nonrelativistic String Theory and Its Applications to Holography)
Reporting period: 2022-09-01 to 2024-08-31
The quest for quantum gravity that unifies general relativity and quantum mechanics poses one of the most profound puzzles in modern theoretical physics and, if resolved, would undoubtedly generate a new revolution in our understanding of the fundamental laws of Nature. The unprecedented and ever-growing experimental observations of gravitational waves, black holes, the cosmic microwave background, and elementary particles are promising to finally allow us to test the predictions of quantum gravity at observable scales.
One promising approach to quantum gravity is inspired by string theory. A powerful nonperturbative description of string theory is given by the quantum mechanics of N × N matrices. At large N , it is famously conjectured that such a matrix quantum mechanics describes nonperturbative quantum gravity in 11 dimensions, which is known as M-theory. Matrix quantum mechanics is also related to Matrix gauge theories, which at large N correspond holographically to quantum gravity in emergent curved spacetime. Solving matrix quantum mechanics at large N promises a quantitative understanding of quantum gravity and black hole physics.
This MSCA project attempts to gain new insights into M-theory and nonperturbative quantum gravity via a novel perspective that involves nonrelativistic behaviors. This project attempts to attack the following questions:
Question 1: Is there a guiding principle for mapping out self-consistent limits of string theory? The success of such a formulation would allow us to enlarge the landscape of Matrix quantum mechanics and holographic duals between field theory and gravity. Patching up these different corners of string theory would eventually deepen our understanding of M-theory, in connection to Question 2 below.
Question 2: M-theory has been mostly accessed via various corners where it is easier to understand their physical contents. What are the fundamental principles that one may use to define M-theory?
Question 3: How insights from M-theory could be applied to understand puzzles in our observable universe?
In order to address Question 1, this project builds around nonrelativistic string theory as a concrete starting point, where winding strings exchange instantaneous Newton-like interactions as it is for nonrelativistic particles. Based on my studies of extended objects (such as branes of various dimensions) in nonrelativistic string theory and their duals (i.e. two seemingly distinct theories are equivalent to each other), I connect nonrelativistic string theory to other important corners in string and M-theory, including matrix quantum mechanics and different holographic duals. I use this duality web to map out different decoupling nonperturbative corners of string and M-theory.
For Question 2, I study the quantization of quantum critical membrane, which provides a candidate high-energy completion of the membrane in M-theory.
Finally, in connection to Question 3, I also explore an application of M-theory to axion universe, which may provide new insights towards dark matter and the strong CP problem in particle physics and cosmology.
The objective of this problem concerns the fundamental laws of physics. The holographical aspects have potential impacts on condensed matter physics.
One promising approach to quantum gravity is inspired by string theory. A powerful nonperturbative description of string theory is given by the quantum mechanics of N × N matrices. At large N , it is famously conjectured that such a matrix quantum mechanics describes nonperturbative quantum gravity in 11 dimensions, which is known as M-theory. Matrix quantum mechanics is also related to Matrix gauge theories, which at large N correspond holographically to quantum gravity in emergent curved spacetime. Solving matrix quantum mechanics at large N promises a quantitative understanding of quantum gravity and black hole physics.
This MSCA project attempts to gain new insights into M-theory and nonperturbative quantum gravity via a novel perspective that involves nonrelativistic behaviors. This project attempts to attack the following questions:
Question 1: Is there a guiding principle for mapping out self-consistent limits of string theory? The success of such a formulation would allow us to enlarge the landscape of Matrix quantum mechanics and holographic duals between field theory and gravity. Patching up these different corners of string theory would eventually deepen our understanding of M-theory, in connection to Question 2 below.
Question 2: M-theory has been mostly accessed via various corners where it is easier to understand their physical contents. What are the fundamental principles that one may use to define M-theory?
Question 3: How insights from M-theory could be applied to understand puzzles in our observable universe?
In order to address Question 1, this project builds around nonrelativistic string theory as a concrete starting point, where winding strings exchange instantaneous Newton-like interactions as it is for nonrelativistic particles. Based on my studies of extended objects (such as branes of various dimensions) in nonrelativistic string theory and their duals (i.e. two seemingly distinct theories are equivalent to each other), I connect nonrelativistic string theory to other important corners in string and M-theory, including matrix quantum mechanics and different holographic duals. I use this duality web to map out different decoupling nonperturbative corners of string and M-theory.
For Question 2, I study the quantization of quantum critical membrane, which provides a candidate high-energy completion of the membrane in M-theory.
Finally, in connection to Question 3, I also explore an application of M-theory to axion universe, which may provide new insights towards dark matter and the strong CP problem in particle physics and cosmology.
The objective of this problem concerns the fundamental laws of physics. The holographical aspects have potential impacts on condensed matter physics.
This project has already led to 7 publications during the reporting period. I have found a new realization of the SL(2,Z) duality in nonrelativistic string and M-theory, which led to the following publications: (1) branched SL(2,ℤ) duality, JHEP 10 (2022) 131, (2) non-Lorentzian IIB supergravity from a polynomial realization of SL(2, ℝ), JHEP 12 (2023) 022, and (3) anisotropic compactification of nonrelativistic M-theory, JHEP 11 (2023) 135. This work makes the transition from nonrelativistic string theory to the study of matrix quantum mechanics. I also published a paper on a novel worldsheet theory for quantum critical membranes in spacetime with two metrics ((4) renormalization of supersymmetric Lifshitz sigma models, JHEP 03 (2023) 008). Finally, in two of my latest publications with the PI (Prof. Obers) ((5) worldsheet formalism for decoupling limits in string theory, JHEP 07 (2024) 102; (6) unification of decoupling limits in string and M theory, Phys.Rev.Lett. 132 (2024) 16, 161603), I studied the duality web unifying important limits in string/M-theory, and established new connections to important theories. I was also invited to write a review article, which has been accepted to J. Phys. A ((7) exact approaches on the string worldsheet, arXiv:2312.12930 [hep-th], where I was responsible for section 7. Matrix theory and the string worldsheet).
I am now finishing the manuscripts for the further results produced during the reporting period, and will publish 4 more papers soon. This includes (1) matrix theory reloaded I: a BPS road to holography, (2) axions, three-forms, and M-theory, (3) conformal mapping of non-Lorentzian geometries in SU(1,2) conformal field theory, (4) heterotic string sigma models: discrete light cone quantization and its TTbar deformation. I also anticipate 3 more papers in the future with the main results obtained during the reporting period (with the PI, Prof. Obers): (1) Matrix theory reloaded II: non-Lorentzian geometries and split U-duality, (2) matrix theory reloaded III: multicritical M-theory from double DLCQs, and (3) tensionless and Carrollian strings from Matrix theory.
Other disseminations include the 1 organized workshop, 9 conference talks, and 14 seminars.
I am now finishing the manuscripts for the further results produced during the reporting period, and will publish 4 more papers soon. This includes (1) matrix theory reloaded I: a BPS road to holography, (2) axions, three-forms, and M-theory, (3) conformal mapping of non-Lorentzian geometries in SU(1,2) conformal field theory, (4) heterotic string sigma models: discrete light cone quantization and its TTbar deformation. I also anticipate 3 more papers in the future with the main results obtained during the reporting period (with the PI, Prof. Obers): (1) Matrix theory reloaded II: non-Lorentzian geometries and split U-duality, (2) matrix theory reloaded III: multicritical M-theory from double DLCQs, and (3) tensionless and Carrollian strings from Matrix theory.
Other disseminations include the 1 organized workshop, 9 conference talks, and 14 seminars.
I have made a series of progress beyond the state of the art: I uncovered a sizeable duality web centered around matrix quantum mechanics and nonrelativistic string theory, and unveiled new matrix theories and (nonrelativistic) holographic dualities, with potential connections to condensed matter physics. I also realized novel SL(2,Z) duality in nonrelativistic string theory, which leads to the discovery of universal features in different corners of the duality web. Based on these progresses, I established new connections among exotic string theories, including the ones that are nonrelativistic, tensionless, ambitwistor, and Carrollian. Furthermore, I showed how they are related to matrix quantum mechanics. I also revealed the non-Lorentzian geometry underlying matrix theories and clarified their role in the context of holography, and found new black hole solutions. These findings do not only fulfil the original goals set in the proposal, but also reach for a much larger framework impacting both holography and M-theory.
Moreover, I also made contributions from other aspects that have direct synergies with the original goal: First, I built up an explicitly conformal mapping between non-Lorentzian geometries for nonrelativistic CFTs. Second, I proposed a new M-theory inspired model for axions, impacting cosmology and particle physics. Third, I studied the discrete light cone quantization of heterotic string theory and derived the relevant sigma models, which further enlarge the scope of the aforementioned framework. Finally, I derived the renormalization group flows for the matter sector in the theory of quantum critical membrane, with potential impacts on the fundamental principles of M-theory.
The progress made in this project is pure theoretical and mostly has impact on the fundamental laws in physics and how we perceive the nature, instead of direct socio-economic impact.
Moreover, I also made contributions from other aspects that have direct synergies with the original goal: First, I built up an explicitly conformal mapping between non-Lorentzian geometries for nonrelativistic CFTs. Second, I proposed a new M-theory inspired model for axions, impacting cosmology and particle physics. Third, I studied the discrete light cone quantization of heterotic string theory and derived the relevant sigma models, which further enlarge the scope of the aforementioned framework. Finally, I derived the renormalization group flows for the matter sector in the theory of quantum critical membrane, with potential impacts on the fundamental principles of M-theory.
The progress made in this project is pure theoretical and mostly has impact on the fundamental laws in physics and how we perceive the nature, instead of direct socio-economic impact.