{"title":"Exact results for scaling dimensions of neutral operators in scalar conformal field theories","authors":"Oleg Antipin, Jahmall Bersini, Francesco Sannino","doi":"10.1103/physrevd.111.l041701","DOIUrl":null,"url":null,"abstract":"We determine the scaling dimension Δ</a:mi>n</a:mi></a:msub></a:math> for the class of composite operators <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><d:msup><d:mi>ϕ</d:mi><d:mi>n</d:mi></d:msup></d:math> in the <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><f:mi>λ</f:mi><f:msup><f:mi>ϕ</f:mi><f:mn>4</f:mn></f:msup></f:math> theory in <h:math xmlns:h=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><h:mi>d</h:mi><h:mo>=</h:mo><h:mn>4</h:mn><h:mo>−</h:mo><h:mi>ε</h:mi></h:math> taking the double scaling limit <j:math xmlns:j=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><j:mi>n</j:mi><j:mo stretchy=\"false\">→</j:mo><j:mi>∞</j:mi></j:math> and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:mi>λ</m:mi><m:mo stretchy=\"false\">→</m:mo><m:mn>0</m:mn></m:math> with fixed <p:math xmlns:p=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><p:mi>λ</p:mi><p:mi>n</p:mi></p:math> via a semiclassical approach. Our results resum the leading power of <r:math xmlns:r=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><r:mi>n</r:mi></r:math> at any loop order. In the small <t:math xmlns:t=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><t:mi>λ</t:mi><t:mi>n</t:mi></t:math> regime we reproduce the known diagrammatic results and predict the infinite series of higher-order terms. For intermediate values of <v:math xmlns:v=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><v:mi>λ</v:mi><v:mi>n</v:mi></v:math> we find that <x:math xmlns:x=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><x:msub><x:mi mathvariant=\"normal\">Δ</x:mi><x:mi>n</x:mi></x:msub><x:mo>/</x:mo><x:mi>n</x:mi></x:math> increases monotonically approaching a (</ab:mo>λ</ab:mi>n</ab:mi>)</ab:mo>1</ab:mn>/</ab:mo>3</ab:mn></ab:mrow></ab:msup></ab:math> behavior in the <eb:math xmlns:eb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><eb:mi>λ</eb:mi><eb:mi>n</eb:mi><eb:mo stretchy=\"false\">→</eb:mo><eb:mi>∞</eb:mi></eb:math> limit. We further generalize our results to neutral operators in the <hb:math xmlns:hb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><hb:msup><hb:mi>ϕ</hb:mi><hb:mn>4</hb:mn></hb:msup></hb:math> in <jb:math xmlns:jb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><jb:mi>d</jb:mi><jb:mo>=</jb:mo><jb:mn>4</jb:mn><jb:mo>−</jb:mo><jb:mi>ε</jb:mi></jb:math>, <lb:math xmlns:lb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><lb:msup><lb:mi>ϕ</lb:mi><lb:mn>3</lb:mn></lb:msup></lb:math> in <nb:math xmlns:nb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><nb:mi>d</nb:mi><nb:mo>=</nb:mo><nb:mn>6</nb:mn><nb:mo>−</nb:mo><nb:mi>ε</nb:mi></nb:math>, and <pb:math xmlns:pb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><pb:msup><pb:mi>ϕ</pb:mi><pb:mn>6</pb:mn></pb:msup></pb:math> in <rb:math xmlns:rb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><rb:mi>d</rb:mi><rb:mo>=</rb:mo><rb:mn>3</rb:mn><rb:mo>−</rb:mo><rb:mi>ε</rb:mi></rb:math> theories with <tb:math xmlns:tb=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><tb:mi>O</tb:mi><tb:mo stretchy=\"false\">(</tb:mo><tb:mi>N</tb:mi><tb:mo stretchy=\"false\">)</tb:mo></tb:math> symmetry. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"66 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.l041701","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We determine the scaling dimension Δn for the class of composite operators ϕn in the λϕ4 theory in d=4−ε taking the double scaling limit n→∞ and λ→0 with fixed λn via a semiclassical approach. Our results resum the leading power of n at any loop order. In the small λn regime we reproduce the known diagrammatic results and predict the infinite series of higher-order terms. For intermediate values of λn we find that Δn/n increases monotonically approaching a (λn)1/3 behavior in the λn→∞ limit. We further generalize our results to neutral operators in the ϕ4 in d=4−ε, ϕ3 in d=6−ε, and ϕ6 in d=3−ε theories with O(N) symmetry. Published by the American Physical Society2025
我们通过半经典方法确定了在λ 4理论中，在d=4−ε条件下，取双标度极限n→∞和λ→0且λn固定的复合算子类的标度维Δn。我们的结果恢复了n在任何循环阶的导幂。在λn小范围内，我们再现了已知的图解结果，并预测了高阶项的无穷级数。对于λn的中间值，我们发现Δn/n在λn→∞极限下单调增加，接近于（λn）1/3的行为。我们进一步将我们的结果推广到具有O(N)对称性的ϕ4 in d=4−ε， ϕ3 in d=6−ε和ϕ6 in d=3−ε理论中的中立算子。2025年由美国物理学会出版
期刊介绍：
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
