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Quantum Field Theory in Singular Limits
High Energy Physics - Theory · Submitted 3 Dec 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories.
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The abstract, sentence by sentence
This is a short summary of the phase structure of vector O(N) symmetric quantum field theories in a singular limit, the double scaling limit.It is motivated by the fact that summing up dynamically triangulated random surfaces using Feynman graphs of the O(N) matrix model results in a genus expansion and it provides,in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced. The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories. In this limit all orders in {1\over N} are of equal importance since at each order infrared divergences compensate for the decrease in powers of {1\over N}. The infrared divergences are due to the tuning of the strength of the force {g \to g_c} between the O(N) quanta so that a massless O(N) singlet appears in the spectrum. At the critical dimension an interesting phase structure is revealed, the massless excitation has the expected physical meaning: it is the Goldston boson of spontaneous breaking of scale invariance - the dilaton.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This is a short summary of the phase structure of vector O(N) symmetric quantum field theories in a singular limit, the double scaling limit.It is motivated by the fact that summing up dynamically triangulated random surfaces using Feynman graphs of the O(N) matrix model results in a genus expansion and it provides,in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced. | background 0.65 | 0.32 | 0.09 | asserted 0.91 |
| s1 | The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories. | contribution 0.45 | 0.23 | 0.72 | asserted 0.95 |
| s2 | In this limit all orders in {1\over N} are of equal importance since at each order infrared divergences compensate for the decrease in powers of {1\over N}. | result 0.66 | 0.40 | 0.15 | asserted 1.00 |
| s3 | The infrared divergences are due to the tuning of the strength of the force {g \to g_c} between the O(N) quanta so that a massless O(N) singlet appears in the spectrum. | interpretation 0.59 | 0.31 | 0.08 | asserted 1.00 |
| s4 | At the critical dimension an interesting phase structure is revealed, the massless excitation has the expected physical meaning: it is the Goldston boson of spontaneous breaking of scale invariance - the dilaton. | interpretation 0.79 | 0.60 | 0.26 | asserted 1.00 |
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Original abstract
This is a short summary of the phase structure of vector O(N) symmetric quantum field theories in a singular limit, the double scaling limit.It is motivated by the fact that summing up dynamically triangulated random surfaces using Feynman graphs of the O(N) matrix model results in a genus expansion and it provides,in some sense, a nonperturbative treatment of string theory when the double scaling limit is enforced. The main point emphasized here is that this formal singular limit, recently discussed mainly in d=0 O(N) matrix models, has an intriguing physical meaning in d>2 O(N) vector theories. In this limit all orders in {1\over N} are of equal importance since at each order infrared divergences compensate for the decrease in powers of {1\over N}. The infrared divergences are due to the tuning of the strength of the force {g \to g_c} between the O(N) quanta so that a massless O(N) singlet appears in the spectrum. At the critical dimension an interesting phase structure is revealed, the massless excitation has the expected physical meaning: it is the Goldston boson of spontaneous breaking of scale invariance - the dilaton.
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