What is なく doing in this sentence?

Question

While reading the light novel for 君の名は I came across this sentence in the first chapter:

私は大切な誰かと隙間なくぴったりとくっついている。

Is using なく here equivalent to using ないで or does it have a different meaning altogether?

Answer 1

The なく is the 連用形 of ない used in the sense of:

10 名詞に付いて、否定の意を含む形容詞をつくる。「こころ―・い」「違い―・い」「面目 (めんぼく) ―・い」　(デジタル大辞泉)

ない can be attached to a noun, forming an i-adjective with a negative meaning ("without~~"). A few more examples: 「[絶]{た}え[間]{ま}ない」「休みない」「[跡形]{あとかた}ない」「[相違]{そうい}ない」

[隙間]{すきま}なく in your example is the 連用形, or the adverbial form, of 「隙間ない」, i.e. 隙間+ない.

Examples: 「絶え間なく」「休みなく」「跡形なく」「[余念]{よねん}なく」「[仕方]{しかた}なく」

Answer 2

Edit

It's come to my attention that the answer by @Chocolate is a much more grounded answer than mine, and admittedly this was the first time I've learned about such a structure in grammatical terms (noun + なく = adverb).

In light of that, I offer my original answer a (not the) way a Japanese language learner can remember or reason out what noun + なくprobably means.

In my personal experience, as a non-native Japanese language learner never having studied the noun + なく form from a book, noun + が + なくて has always been the way I've mentally reasoned out what noun + なく means while communicating with native speakers. One of the first things I (and likely many other Japanese language learners) learned when starting out was the existence of noun + が + ない, so from that building block I would deduce the meaning of noun + なく

In practice it's always helped me correctly understand at least the big-picture meaning, but apparently not the standard grammatical basis.

Original answer

隙間なく

means

隙間がなくて

隙間 is a noun, so the conjugation ○○ないで isn't applicable.